Publications by authors named "Bela M Mulder"

44 Publications

Towards a synthetic cell cycle.

Nat Commun 2021 07 26;12(1):4531. Epub 2021 Jul 26.

Laboratory of Microbiology, Wageningen University, Wageningen, The Netherlands.

Recent developments in synthetic biology may bring the bottom-up generation of a synthetic cell within reach. A key feature of a living synthetic cell is a functional cell cycle, in which DNA replication and segregation as well as cell growth and division are well integrated. Here, we describe different approaches to recreate these processes in a synthetic cell, based on natural systems and/or synthetic alternatives. Although some individual machineries have recently been established, their integration and control in a synthetic cell cycle remain to be addressed. In this Perspective, we discuss potential paths towards an integrated synthetic cell cycle.
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http://dx.doi.org/10.1038/s41467-021-24772-8DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8313558PMC
July 2021

Nonmonotonic swelling and compression dynamics of hydrogels in polymer solutions.

Phys Rev E 2020 Dec;102(6-1):062606

Department of Mechanical Engineering, Materials Technology, Eindhoven University of Technology, 5600MB Eindhoven, Netherlands.

Hydrogels are sponge-like materials that can absorb or expel significant amounts of water. Swelling up from a dried state, they can swell up more than a hundredfold in volume, with the kinetics and the degree of swelling depending sensitively on the physicochemical properties of both the polymer network and the aqueous solvent. In particular, the presence of dissolved macromolecules in the background liquid can have a significant effect, as the macromolecules can exert an additional external osmotic pressure on the hydrogel material, thereby reducing the degree of swelling. In this paper, we have submerged dry hydrogel particles in polymer solutions containing large and small macromolecules. Interestingly, for swelling in the presence of large macromolecules we observe a concentration-dependent overshoot behavior, where the particle volume first continuously increases toward a maximum, after which it decreases again, reaching a lower, equilibrium value. In the presence of smaller macromolecules we do not observe this intriguing overshoot behavior, but instead observe a rapid growth followed by a slowed-down growth. To account for the observed overshoot behavior, we realize that the macromolecules entering the hydrogel network not only lead to a reduction of the osmotic pressure difference, but their presence within the network also affects the swelling behavior through a modification of the solvent-polymer interactions. In this physical picture of the swelling process, the net amount of volume change should thus depend on the magnitudes of both the reduction in osmotic pressure and the change in effective solvent quality associated with the macromolecules entering the pores of the hydrogel network. We develop a phenomenological model that incorporates both of these effects. Using this model we are able to account for both the swelling and compression kinetics of hydrogels within aqueous polymer solutions, as a function of the size of the dissolved macromolecules and of their effect on the effective solvent quality.
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http://dx.doi.org/10.1103/PhysRevE.102.062606DOI Listing
December 2020

Compression and swelling of hydrogels in polymer solutions: A dominant-mode model.

Phys Rev E 2020 Dec;102(6-1):062607

Institute AMOLF, Theory of Biomolecular Matter, Science Park 104, 1098XG Amsterdam, The Netherlands.

The swelling and compression of hydrogels in polymer solutions can be understood by considering hydrogel-osmolyte-solvent interactions which determine the osmotic pressure difference between the inside and the outside of a hydrogel particle and the changes in effective solvent quality for the hydrogel network. Using the theory of poroelasticity, we find the exact solution to hydrogel dynamics in a dilute polymer solution, which quantifies the effect of diffusion and partitioning of osmolyte and the related solvent quality change to the volumetric changes of the hydrogel network. By making a dominant-mode assumption, we propose a model for the swelling and compression dynamics of (spherical) hydrogels in concentrated polymer solutions. Osmolyte diffusion induces a biexponential response in the size of the hydrogel radius, whereas osmolyte partitioning and solvent quality effects induce monoexponential responses. Comparison of the dominant-mode model to experiments provides reasonable values for the compressive bulk modulus of a hydrogel particle, the permeability of the hydrogel network, and the diffusion constant of osmolyte molecules inside the hydrogel network. Our model shows that hydrogel-osmolyte interactions can be described in a conceptually simple manner, while still capturing the rich (de)swelling behaviors observed in experiments. We expect our approach to provide a roadmap for further research into and applications of hydrogel dynamics induced by, for example, changes in the temperature and the pH.
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http://dx.doi.org/10.1103/PhysRevE.102.062607DOI Listing
December 2020

Microtubule-based actin transport and localization in a spherical cell.

R Soc Open Sci 2020 Nov 11;7(11):201730. Epub 2020 Nov 11.

AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands.

The interaction between actin filaments and microtubules is crucial for many eukaryotic cellular processes, such as, among others, cell polarization, cell motility and cellular wound healing. The importance of this interaction has long been recognized, yet very little is understood about both the underlying mechanisms and the consequences for the spatial (re)organization of the cellular cytoskeleton. At the same time, understanding the causes and the consequences of the interaction between different biomolecular components are key questions for research involving reconstituted biomolecular systems, especially in the light of current interest in creating minimal synthetic cells. In this light, recent experiments have shown that the actin-microtubule interaction mediated by the cytolinker TipAct, which binds to actin lattice and microtubule tips, causes the directed transport of actin filaments. We develop an analytical theory of dynamically unstable microtubules, nucleated from the centre of a spherical cell, in interaction with actin filaments. We show that, depending on the balance between the diffusion of unbound actin filaments and propensity to bind microtubules, actin is either concentrated in the centre of the cell, where the density of microtubules is highest, or becomes localized to the cell cortex.
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http://dx.doi.org/10.1098/rsos.201730DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7735335PMC
November 2020

Critical threshold for microtubule amplification through templated severing.

Phys Rev E 2020 May;101(5-1):052405

AMOLF, Science Park 104, 1098XG Amsterdam, Netherlands.

The cortical microtubule array of dark-grown hypocotyl cells of plant seedlings undergoes a striking, and developmentally significant, reorientation on exposure to light. This process is driven by the exponential amplification of a population of longitudinal microtubules, created by severing events localized at crossovers with the microtubules of the pre-existing transverse array. We present a dynamic one-dimensional model for microtubule amplification through this type of templated severing. We focus on the role of the probability of immediate stabilization-after-severing of the newly created lagging microtubule, observed to be a characteristic feature of the reorientation process. Employing stochastic simulations, we show that in the dynamic regime of unbounded microtubule growth, a finite value of this probability is not required for amplification to occur but does strongly influence the degree of amplification and hence the speed of the reorientation process. In contrast, in the regime of bounded microtubule growth, we show that amplification only occurs above a critical threshold. We construct an approximate analytical theory, based on a priori limiting the number of crossover events considered, which allows us to predict the observed critical value of the stabilization-after-severing probability with reasonable accuracy.
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http://dx.doi.org/10.1103/PhysRevE.101.052405DOI Listing
May 2020

Poroelasticity of (bio)polymer networks during compression: theory and experiment.

Soft Matter 2020 Feb 10;16(5):1298-1305. Epub 2020 Jan 10.

AMOLF, Theory of Biomolecular Matter, Science Park 104, 1098XG Amsterdam, The Netherlands.

Soft living tissues like cartilage can be considered as biphasic materials comprising a fibrous complex biopolymer network and a viscous background liquid. Here, we show by a combination of experiment and theoretical analysis that both the hydraulic permeability and the elastic properties of (bio)polymer networks can be determined with simple ramp compression experiments in a commercial rheometer. In our approximate closed-form solution of the poroelastic equations of motion, we find the normal force response during compression as a combination of network stress and fluid pressure. Choosing fibrin as a biopolymer model system with controllable pore size, measurements of the full time-dependent normal force during compression are found to be in excellent agreement with the theoretical calculations. The inferred elastic response of large-pore (μm) fibrin networks depends on the strain rate, suggesting a strong interplay between network elasticity and fluid flow. Phenomenologically extending the calculated normal force into the regime of nonlinear elasticity, we find strain-stiffening of small-pore (sub-μm) fibrin networks to occur at an onset average tangential stress at the gel-plate interface that depends on the polymer concentration in a power-law fashion. The inferred permeability of small-pore fibrin networks scales approximately inverse squared with the fibrin concentration, implying with a microscopic cubic lattice model that the number of protofibrils per fibrin fiber cross-section decreases with protein concentration. Our theoretical model provides a new method to obtain the hydraulic permeability and the elastic properties of biopolymer networks and hydrogels with simple compression experiments, and paves the way to study the relation between fluid flow and elasticity in biopolymer networks during dynamical compression.
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http://dx.doi.org/10.1039/c9sm01973aDOI Listing
February 2020

Colloidal Liquid Crystals Confined to Synthetic Tactoids.

Sci Rep 2019 12 31;9(1):20391. Epub 2019 Dec 31.

AMOLF, Department of Living Matter, Amsterdam, 1098XG, The Netherlands.

When a liquid crystal forming particles are confined to a spatial volume with dimensions comparable to that of their own size, they face a complex trade-off between their global tendency to align and the local constraints imposed by the boundary conditions. This interplay may lead to a non-trivial orientational patterns that strongly depend on the geometry of the confining volume. This novel regime of liquid crystalline behavior can be probed with colloidal particles that are macro-aggregates of biomolecules. Here we study director fields of filamentous fd-viruses in quasi-2D lens-shaped chambers that mimic the shape of tactoids, the nematic droplets that form during isotropic-nematic phase separation. By varying the size and aspect ratio of the chambers we force these particles into confinements that vary from circular to extremely spindle-like shapes and observe the director field using fluorescence microscopy. In the resulting phase diagram, next to configurations predicted earlier for 3D tactoids, we find a number of novel configurations. Using Monte Carlo Simulations, we show that these novel states are metastable, yet long-lived. Their multiplicity can be explained by the co-existence of multiple dynamic relaxation pathways leading to the final stable states.
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http://dx.doi.org/10.1038/s41598-019-56729-9DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6938498PMC
December 2019

From plasmodesma geometry to effective symplasmic permeability through biophysical modelling.

Elife 2019 11 22;8. Epub 2019 Nov 22.

Centre for Plant Science, University of Leeds, Leeds, United Kingdom.

Regulation of molecular transport via intercellular channels called plasmodesmata (PDs) is important for both coordinating developmental and environmental responses among neighbouring cells, and isolating (groups of) cells to execute distinct programs. Cell-to-cell mobility of fluorescent molecules and PD dimensions (measured from electron micrographs) are both used as methods to predict PD transport capacity (i.e., effective symplasmic permeability), but often yield very different values. Here, we build a theoretical bridge between both experimental approaches by calculating the effective symplasmic permeability from a geometrical description of individual PDs and considering the flow towards them. We find that a dilated central region has the strongest impact in thick cell walls and that clustering of PDs into pit fields strongly reduces predicted permeabilities. Moreover, our open source multi-level model allows to predict PD dimensions matching measured permeabilities and add a functional interpretation to structural differences observed between PDs in different cell walls.
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http://dx.doi.org/10.7554/eLife.49000DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6994222PMC
November 2019

Gravity-driven syneresis in model low-fat mayonnaise.

Soft Matter 2019 Nov;15(46):9474-9481

Physical Chemistry and Soft Matter, Wageningen University and Research, Stippeneng 4, 6708 WE, Wageningen, The Netherlands.

Low-fat food products often contain natural, edible polymers to retain the desired mouth feel and elasticity of their full-fat counterparts. This type of product, however, can suffer from syneresis: densification due to the expulsion of fluid. Gaining insight into the physical principles governing syneresis in such soft hybrid dispersions remains a challenge from a theoretical perspective, as experimental data are needed to establish a basis. We record non-accelerated syneresis in a model system for low-fat mayonnaise: a colloid polymer mixture, consisting of oil in water emulsion with starch in the aqueous phase. We find the flow rate of expelled fluid to be proportional to the difference in hydrostatic pressure over the system. The osmotic pressure of the added starch, while being higher than the hydrostatic pressure, does not prevent syneresis because the soluble starch is lost to the expelled fluid. From these findings, we conclude that forced syneresis in these systems can be described as a gravity-driven porous flow through the densely packed emulsion, explainable with a model based on Darcy's law.
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http://dx.doi.org/10.1039/c9sm01097aDOI Listing
November 2019

Confinement and crowding control the morphology and dynamics of a model bacterial chromosome.

Soft Matter 2019 Mar;15(12):2677-2687

Indian Institute of Technology Hyderabad, Kandi, Sangareddy 502285, Telangana, India.

Motivated by recent experiments probing the shape, size and dynamics of bacterial chromosomes in growing cells, we consider a polymer model consisting of a circular backbone to which side-loops are attached, confined to a cylindrical cell. Such a model chromosome spontaneously adopts a helical shape, which is further compacted by molecular crowders to occupy a nucleoid-like sub-volume of the cell. With increasing cell length, the longitudinal size of the chromosome increases in a non-linear fashion until finally saturating, its morphology gradually opening up while displaying a changing number of helical turns. For shorter cells, the chromosome extension varies non-monotonically with cell size, which we show is associated with a radial to longitudinal spatial reordering of the crowders. Confinement and crowders constrain chain dynamics leading to anomalous diffusion. While the scaling exponent for the mean squared displacement of center of mass grows and saturates with cell length, that of individual loci displays a broad distribution with a sharp maximum.
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http://dx.doi.org/10.1039/c8sm02092bDOI Listing
March 2019

CLASP stabilization of plus ends created by severing promotes microtubule creation and reorientation.

J Cell Biol 2019 01 30;218(1):190-205. Epub 2018 Oct 30.

Department of Plant Biology, Carnegie Institution for Science, Stanford, CA

Central to the building and reorganizing cytoskeletal arrays is creation of new polymers. Although nucleation has been the major focus of study for microtubule generation, severing has been proposed as an alternative mechanism to create new polymers, a mechanism recently shown to drive the reorientation of cortical arrays of higher plants in response to blue light perception. Severing produces new plus ends behind the stabilizing GTP-cap. An important and unanswered question is how these ends are stabilized in vivo to promote net microtubule generation. Here we identify the conserved protein CLASP as a potent stabilizer of new plus ends created by katanin severing in plant cells. mutants are defective in cortical array reorientation. In these mutants, both rescue of shrinking plus ends and the stabilization of plus ends immediately after severing are reduced. Computational modeling reveals that it is the specific stabilization of severed ends that best explains CLASP's function in promoting microtubule amplification by severing and array reorientation.
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http://dx.doi.org/10.1083/jcb.201805047DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6314540PMC
January 2019

Molecular Dynamics Simulation of a Feather-Boa Model of a Bacterial Chromosome.

Methods Mol Biol 2018 ;1837:403-415

Institute AMOLF, Science Park 104, Amsterdam, 1098 XG, The Netherlands.

The chromosome of a bacterium consists of a mega-base pair long circular DNA, which self-organizes within the micron-sized bacterial cell volume, compacting itself by three orders of magnitude. Unlike in eukaryotes, it lacks a nuclear membrane, and freely floats in the cytosol confined by the cell membrane. It is believed that strong confinement, cross-linking by associated proteins, and molecular crowding all contribute to determine chromosome size and morphology. Modeling the chromosome simply as a circular polymer decorated with closed side-loops in a cylindrical confining volume, has been shown to already recapture some of the salient properties observed experimentally. Here, we describe how a computer simulation can be set up to study structure and dynamics of bacterial chromosomes using this model.
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http://dx.doi.org/10.1007/978-1-4939-8675-0_20DOI Listing
April 2019

A computational framework for cortical microtubule dynamics in realistically shaped plant cells.

PLoS Comput Biol 2018 02 2;14(2):e1005959. Epub 2018 Feb 2.

Department of Living Matter, Institute AMOLF, Amsterdam, The Netherlands.

Plant morphogenesis is strongly dependent on the directional growth and the subsequent oriented division of individual cells. It has been shown that the plant cortical microtubule array plays a key role in controlling both these processes. This ordered structure emerges as the collective result of stochastic interactions between large numbers of dynamic microtubules. To elucidate this complex self-organization process a number of analytical and computational approaches to study the dynamics of cortical microtubules have been proposed. To date, however, these models have been restricted to two dimensional planes or geometrically simple surfaces in three dimensions, which strongly limits their applicability as plant cells display a wide variety of shapes. This limitation is even more acute, as both local as well as global geometrical features of cells are expected to influence the overall organization of the array. Here we describe a framework for efficiently simulating microtubule dynamics on triangulated approximations of arbitrary three dimensional surfaces. This allows the study of microtubule array organization on realistic cell surfaces obtained by segmentation of microscopic images. We validate the framework against expected or known results for the spherical and cubical geometry. We then use it to systematically study the individual contributions of global geometry, cell-edge induced catastrophes and cell-face induced stability to array organization in a cuboidal geometry. Finally, we apply our framework to analyze the highly non-trivial geometry of leaf pavement cells of Arabidopsis thaliana, Nicotiana benthamiana and Hedera helix. We show that our simulations can predict multiple features of the microtubule array structure in these cells, revealing, among others, strong constraints on the orientation of division planes.
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http://dx.doi.org/10.1371/journal.pcbi.1005959DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5812663PMC
February 2018

SPR2 protects minus ends to promote severing and reorientation of plant cortical microtubule arrays.

J Cell Biol 2018 03 16;217(3):915-927. Epub 2018 Jan 16.

Department of Plant Biology, Carnegie Institution for Science, Stanford, CA

The cortical microtubule arrays of higher plants are organized without centrosomes and feature treadmilling polymers that are dynamic at both ends. The control of polymer end stability is fundamental for the assembly and organization of cytoskeletal arrays, yet relatively little is understood about how microtubule minus ends are controlled in acentrosomal microtubule arrays, and no factors have been identified that act at the treadmilling minus ends in higher plants. Here, we identify SPIRAL2 (SPR2) as a protein that tracks minus ends and protects them against subunit loss. SPR2 function is required to facilitate the rapid reorientation of plant cortical arrays as stimulated by light perception, a process that is driven by microtubule severing to create a new population of microtubules. Quantitative live-cell imaging and computer simulations reveal that minus protection by SPR2 acts by an unexpected mechanism to promote the lifetime of potential SPR2 severing sites, increasing the likelihood of severing and thus the rapid amplification of the new microtubule array.
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http://dx.doi.org/10.1083/jcb.201708130DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5839793PMC
March 2018

The Landau-de Gennes approach revisited: A minimal self-consistent microscopic theory for spatially inhomogeneous nematic liquid crystals.

J Chem Phys 2017 Dec;147(24):244505

Institute AMOLF, Science Park 104, 1098XG Amsterdam, The Netherlands.

We design a novel microscopic mean-field theory of inhomogeneous nematic liquid crystals formulated entirely in terms of the tensor order parameter field. It combines the virtues of the Landau-de Gennes approach in allowing both the direction and magnitude of the local order to vary, with a self-consistent treatment of the local free-energy valid beyond the small order parameter limit. As a proof of principle, we apply this theory to the well-studied problem of a colloid dispersed in a nematic liquid crystal by including a tunable wall coupling term. For the two-dimensional case, we investigate the organization of the liquid crystal and the position of the point defects as a function of the strength of the coupling constant.
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http://dx.doi.org/10.1063/1.4993574DOI Listing
December 2017

A microtubule-based minimal model for spontaneous and persistent spherical cell polarity.

PLoS One 2017 20;12(9):e0184706. Epub 2017 Sep 20.

Systems Biophysics Department, Institute AMOLF, Amsterdam, the Netherlands.

We propose a minimal model for the spontaneous and persistent generation of polarity in a spherical cell based on dynamic microtubules and a single mobile molecular component. This component, dubbed the polarity factor, binds to microtubules nucleated from a centrosome located in the center of the cell, is subsequently delivered to the cell membrane, where it diffuses until it unbinds. The only feedback mechanism we impose is that the residence time of the microtubules at the membrane increases with the local density of the polarity factor. We show analytically that this system supports a stable unipolar symmetry-broken state for a wide range of parameters. We validate the predictions of the model by 2D particle-based simulations. Our model provides a route towards the creation of polarity in a minimal cell-like environment using a biochemical reconstitution approach.
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http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0184706PLOS
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5607169PMC
October 2017

How selective severing by katanin promotes order in the plant cortical microtubule array.

Proc Natl Acad Sci U S A 2017 07 19;114(27):6942-6947. Epub 2017 Jun 19.

Systems Biophysics, AMOLF, 1098 XG Amsterdam, The Netherlands.

Plant morphogenesis requires differential and often asymmetric growth. A key role in controlling anisotropic expansion of individual cells is played by the cortical microtubule array. Although highly organized, the array can nevertheless rapidly change in response to internal and external cues. Experiments have identified the microtubule-severing enzyme katanin as a central player in controlling the organizational state of the array. Katanin action is required both for normal alignment and the adaptation of array orientation to mechanical, environmental, and developmental stimuli. How katanin fulfills its controlling role, however, remains poorly understood. On the one hand, from a theoretical perspective, array ordering depends on the "weeding out" of discordant microtubules through frequent catastrophe-inducing collisions among microtubules. Severing would reduce average microtubule length and lifetime, and consequently weaken the driving force for alignment. On the other hand, it has been suggested that selective severing at microtubule crossovers could facilitate the removal of discordant microtubules. Here we show that this apparent conflict can be resolved by systematically dissecting the role of all of the relevant interactions in silico. This procedure allows the identification of the sufficient and necessary conditions for katanin to promote array alignment, stresses the critical importance of the experimentally observed selective severing of the "crossing" microtubule at crossovers, and reveals a hitherto not appreciated role for microtubule bundling. We show how understanding the underlying mechanism can aid with interpreting experimental results and designing future experiments.
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http://dx.doi.org/10.1073/pnas.1702650114DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5502621PMC
July 2017

Finite particle size drives defect-mediated domain structures in strongly confined colloidal liquid crystals.

Nat Commun 2016 06 29;7:12112. Epub 2016 Jun 29.

Department of Systems Biophysics, FOM Institute AMOLF, Science Park 104, 1098XG Amsterdam, The Netherlands.

When liquid crystals are confined to finite volumes, the competition between the surface anchoring imposed by the boundaries and the intrinsic orientational symmetry-breaking of these materials gives rise to a host of intriguing phenomena involving topological defect structures. For synthetic molecular mesogens, like the ones used in liquid-crystal displays, these defect structures are independent of the size of the molecules and well described by continuum theories. In contrast, colloidal systems such as carbon nanotubes and biopolymers have micron-sized lengths, so continuum descriptions are expected to break down under strong confinement conditions. Here, we show, by a combination of computer simulations and experiments with virus particles in tailor-made disk- and annulus-shaped microchambers, that strong confinement of colloidal liquid crystals leads to novel defect-stabilized symmetrical domain structures. These finite-size effects point to a potential for designing optically active microstructures, exploiting the as yet unexplored regime of highly confined liquid crystals.
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http://dx.doi.org/10.1038/ncomms12112DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4931596PMC
June 2016

Biological filaments: Self-healing microtubules.

Nat Mater 2015 Nov;14(11):1080-1

Department of Systems Biophysics, FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands.

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http://dx.doi.org/10.1038/nmat4460DOI Listing
November 2015

Defect structures mediate the isotropic-nematic transition in strongly confined liquid crystals.

Soft Matter 2015 Jan;11(3):608-14

FOM Institute AMOLF, Science Park 104, 1098XG Amsterdam, The Netherlands.

Using Monte Carlo simulations, we study rod-like lyotropic liquid crystals confined to a square slab-like geometry with lateral dimensions comparable to the length of the particles. We observe that this system develops linear defect structures upon entering the planar nematic phase. These defect structures flank a lens-shaped nematic region oriented along a diagonal of the square box. We interpret these structures as a compromise between the 2-fold order of the bulk nematic phase and the 4-fold order imposed by the lateral boundaries. A simple Onsager-type theory that effectively implements these competing tendencies is used to model the phase behavior in the center of the box and shows that the free-energy cost of forming the defect structures strongly offsets the transition-inducing effects of both the transverse and lateral confinement.
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http://dx.doi.org/10.1039/c4sm02087aDOI Listing
January 2015

The effect of anisotropic microtubule-bound nucleations on ordering in the plant cortical array.

Bull Math Biol 2014 Nov 28;76(11):2907-22. Epub 2014 Oct 28.

Department of Systems Biophysics, FOM Institute AMOLF, Science Park 104, 1098 XG, Amsterdam, The Netherlands.

The highly orientationally ordered cortical microtubule array in plant cells is a key component for cell growth and development. Recent experimental and computational work has shown that the anisotropic nucleation of new microtubules from pre-existing microtubules has a major effect on the alignment process. We formulate a theoretical model to investigate the role of the microtubule-bound nucleation on the self-organization of the dynamical cortical microtubules. A bifurcation analysis of the stability of the disordered phase of the model reveals that the effective degree of co-aligned nucleation is the main determinant of the location of the transition. Increased co-aligned nucleation creates a positive feedback effect on the ordering process that can significantly widen the ordered region. We validate these predictions by comparing to the results of particle-based simulations.
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http://dx.doi.org/10.1007/s11538-014-0039-3DOI Listing
November 2014

Colloidal liquid crystals in rectangular confinement: theory and experiment.

Soft Matter 2014 Oct 26;10(39):7865-73. Epub 2014 Aug 26.

Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK.

We theoretically and experimentally study nematic liquid crystal equilibria within shallow rectangular wells. We model the wells within a two-dimensional Oseen-Frank framework, with strong tangent anchoring, and obtain explicit analytical expressions for the director fields and energies of the 'diagonal' and 'rotated' solutions reported in the literature. These expressions separate the leading-order defect energies from the bulk distortion energy for both families of solutions. The continuum Oseen-Frank study is complemented by a microscopic mean-field approach. We numerically minimize the mean-field functional, including the effects of weak anchoring, variable order and random initial conditions. In particular, these simulations suggest the existence of higher-energy metastable states with internal defects. We compare our theoretical results to experimental director profiles, obtained using two types of filamentous virus particles, wild-type fd-virus and a modified stiffer variant (Y21M), which display nematic ordering in rectangular chambers, as found by confocal scanning laser microscopy. We combine our analytical energy expressions with experimentally recorded frequencies of the different equilibrium states to obtain explicit estimates for the extrapolation length, defined to be the ratio of the nematic elastic constant to the anchoring coefficient, of the fd-virus.
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http://dx.doi.org/10.1039/c4sm01123fDOI Listing
October 2014

Microtubule networks for plant cell division.

Syst Synth Biol 2014 Sep 2;8(3):187-94. Epub 2014 Apr 2.

Laboratory of Cell Biology, Wageningen University, Droevendaalsesteeg 1, 6708 PB Wageningen, The Netherlands.

During cytokinesis the cytoplasm of a cell is divided to form two daughter cells. In animal cells, the existing plasma membrane is first constricted and then abscised to generate two individual plasma membranes. Plant cells on the other hand divide by forming an interior dividing wall, the so-called cell plate, which is constructed by localized deposition of membrane and cell wall material. Construction starts in the centre of the cell at the locus of the mitotic spindle and continues radially towards the existing plasma membrane. Finally the membrane of the cell plate and plasma membrane fuse to form two individual plasma membranes. Two microtubule-based cytoskeletal networks, the phragmoplast and the pre-prophase band (PPB), jointly control cytokinesis in plants. The bipolar microtubule array of the phragmoplast regulates cell plate deposition towards a cortical position that is templated by the ring-shaped microtubule array of the PPB. In contrast to most animal cells, plants do not use centrosomes as foci of microtubule growth initiation. Instead, plant microtubule networks are striking examples of self-organizing systems that emerge from physically constrained interactions of dispersed microtubules. Here we will discuss how microtubule-based activities including growth, shrinkage, severing, sliding, nucleation and bundling interrelate to jointly generate the required ordered structures. Evidence mounts that adapter proteins sense the local geometry of microtubules to locally modulate the activity of proteins involved in microtubule growth regulation and severing. Many of the proteins and mechanisms involved have roles in other microtubule assemblies as well, bestowing broader relevance to insights gained from plants.
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http://dx.doi.org/10.1007/s11693-014-9142-xDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4127175PMC
September 2014

Alignment of nematic and bundled semiflexible polymers in cell-sized confinement.

Soft Matter 2014 Apr;10(14):2354-64

FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands.

The finite size of cells poses severe spatial constraints on the network of semiflexible filaments called the cytoskeleton, a main determinant of cell shape. At the same time, the high packing density of cytoskeletal filaments poses mutual packing constraints. Here we investigate the competition between excluded volume interactions in the bulk and surface packing constraints on the orientational ordering of confined actin filaments as a function of filament density and the presence of crosslinks. We grow fluorescently labeled actin filaments in shallow (thickness dz 3 μm), rectangular microchambers with a systematically varied length (dy between 5 and 100 μm) and in-plane aspect ratio (dx/dy between 1 and 10). We determine the nematic director field by image analysis of fluorescence confocal images. We find that high-density (nematic) solutions respond sensitively to changes in the size and aspect ratio of the chambers. In small chambers (dy ≤ 20 μm), filaments align parallel to the long walls as soon as the aspect ratio is ≥1.5, indicating that surface-induced ordering dominates. In larger chambers, the filaments instead align along the chamber diagonal, indicating that bulk packing constraints dominate. The nematic order parameter is maximal in small and highly anisometric chambers. In contrast to the nematic solutions, low-density (isotropic) solutions are rather insensitive to confinement. Bundled actin solutions behave similarly to nematic solutions, but are less well-ordered. Our observations imply that the orientational order of actin filaments in flat confining geometries is primarily determined by a balance between bulk and surface packing constraints with a minimal effect of the enthalpic cost of filament bending. Our assay provides an interesting platform for the future reconstitution of more complex, active cytoskeletal systems with actively treadmilling filaments or molecular motors.
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http://dx.doi.org/10.1039/c3sm52421cDOI Listing
April 2014

A mechanism for reorientation of cortical microtubule arrays driven by microtubule severing.

Science 2013 Dec 7;342(6163):1245533. Epub 2013 Nov 7.

Department of Plant Biology, Carnegie Institution for Science, Stanford, CA 94305, USA.

Environmental and hormonal signals cause reorganization of microtubule arrays in higher plants, but the mechanisms driving these transitions have remained elusive. The organization of these arrays is required to direct morphogenesis. We discovered that microtubule severing by the protein katanin plays a crucial and unexpected role in the reorientation of cortical arrays, as triggered by blue light. Imaging and genetic experiments revealed that phototropin photoreceptors stimulate katanin-mediated severing specifically at microtubule intersections, leading to the generation of new microtubules at these locations. We show how this activity serves as the basis for a mechanism that amplifies microtubules orthogonal to the initial array, thereby driving array reorientation. Our observations show how severing is used constructively to build a new microtubule array.
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http://dx.doi.org/10.1126/science.1245533DOI Listing
December 2013

Modelling the role of microtubules in plant cell morphology.

Curr Opin Plant Biol 2013 Dec 21;16(6):688-92. Epub 2013 Oct 21.

FOM Institute AMOLF, Science Park 104, 1098XG Amsterdam, The Netherlands.

Normal plant growth requires the anisotropic expansion of cells and the proper orientation of their divisions. Both are controlled by the architecture of the cortical microtubule array. Cortical microtubules interact through frequent collisions. Several modelling studies have shown that these interactions can be sufficient for spontaneous alignment. Further requirements to this self-organization are the homogeneous distribution of microtubule density and reliable control over the array orientation. We review the contribution of computer simulations and mathematical modelling on each of these challenges. These models now provide a good understanding of the basic alignment mechanism and will continue to be very useful tools for investigating more advanced questions, for example how microtubule severing contributes to alignment and array reorientation.
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http://dx.doi.org/10.1016/j.pbi.2013.10.001DOI Listing
December 2013

Cortical microtubule arrays are initiated from a nonrandom prepattern driven by atypical microtubule initiation.

Plant Physiol 2013 Mar 8;161(3):1189-201. Epub 2013 Jan 8.

Laboratory of Cell Biology, Wageningen University, 6708 PB Wageningen, The Netherlands.

The ordered arrangement of cortical microtubules in growing plant cells is essential for anisotropic cell expansion and, hence, for plant morphogenesis. These arrays are dismantled when the microtubule cytoskeleton is rearranged during mitosis and reassembled following completion of cytokinesis. The reassembly of the cortical array has often been considered as initiating from a state of randomness, from which order arises at least partly through self-organizing mechanisms. However, some studies have shown evidence for ordering at early stages of array assembly. To investigate how cortical arrays are initiated in higher plant cells, we performed live-cell imaging studies of cortical array assembly in tobacco (Nicotiana tabacum) Bright Yellow-2 cells after cytokinesis and drug-induced disassembly. We found that cortical arrays in both cases did not initiate randomly but with a significant overrepresentation of microtubules at diagonal angles with respect to the cell axis, which coincides with the predominant orientation of the microtubules before their disappearance from the cell cortex in preprophase. In Arabidopsis (Arabidopsis thaliana) root cells, recovery from drug-induced disassembly was also nonrandom and correlated with the organization of the previous array, although no diagonal bias was observed in these cells. Surprisingly, during initiation, only about one-half of the new microtubules were nucleated from locations marked by green fluorescent protein-γ-tubulin complex protein2-tagged γ-nucleation complexes (γ-tubulin ring complex), therefore indicating that a large proportion of early polymers was initiated by a noncanonical mechanism not involving γ-tubulin ring complex. Simulation studies indicate that the high rate of noncanonical initiation of new microtubules has the potential to accelerate the rate of array repopulation.
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http://dx.doi.org/10.1104/pp.112.204057DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3585589PMC
March 2013

Microtubules interacting with a boundary: mean length and mean first-passage times.

Authors:
Bela M Mulder

Phys Rev E Stat Nonlin Soft Matter Phys 2012 Jul 2;86(1 Pt 1):011902. Epub 2012 Jul 2.

FOM Institute AMOLF, Science Park 104, 1098XG Amsterdam, the Netherlands.

I formulate a dynamical model for microtubules interacting with a catastrophe-inducing boundary. In this model microtubules are either waiting to be nucleated, actively growing or shrinking, or stalled at the boundary. I first determine the steady-state occupation of these various states and the resultant length distribution. Next, I formulate the problem of the mean first-passage time to reach the boundary in terms of an appropriate set of splitting probabilities and conditional mean first-passage times and solve explicitly for these quantities using a differential equation approach. As an application, I revisit a recently proposed search-and-capture model for the interaction between microtubules and target chromosomes [M. Gopalakrishnan and B. S. Govindan, Bull. Math. Biol. 73, 2483 (2011)]. I show how my approach leads to a direct and compact solution of this problem.
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http://dx.doi.org/10.1103/PhysRevE.86.011902DOI Listing
July 2012
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