Microtubule self-organisation by reaction–diffusion processes in miniature cell-sized containers and phospholipid vesicles

Cytoskeletal organization in isolated plant cells under geometry control

The cytoskeleton plays a key role in establishing robust cell shape. In animals, it is well established that cell shape can also influence cytoskeletal organization. Cytoskeletal proteins are well conserved between animal and plant kingdoms; nevertheless, because plant cells exhibit major structural differences to animal cells, the question arises whether the plant cytoskeleton also responds to geometrical cues. Recent numerical simulations predicted that a geometry-based rule is sufficient to explain the microtubule (MT) organization observed in cells. Due to their high flexural rigidity and persistence length of the order of a few millimeters, MTs are rigid over cellular dimensions and are thus expected to align along their long axis if constrained in specific geometries. This hypothesis remains to be tested in cellulo Here, we explore the relative contribution of geometry to the final organization of actin and MT cytoskeletons in single plant cells of Arabidopsis thaliana We show that the cytoskeleton aligns with the long axis of the cells. We find that actin organization relies on MTs but not the opposite. We develop a model of self-organizing MTs in three dimensions, which predicts the importance of MT severing, which we confirm experimentally. This work is a first step toward assessing quantitatively how cellular geometry contributes to the control of cytoskeletal organization in living plant cells.

Multi-scale regulation of cell branching: Modeling morphogenesis

Plant growth and development are driven by extended phases of irreversible cell expansion generating cells that increase in volume from 10- to 100-fold. Some specialized cell types define cortical sites that reinitiate polarized growth and generate branched cell morphology. This structural specialization of individual cells has a major importance for plant adaptation to diverse environments and practical importance in agricultural contexts. The patterns of cell shape are defined by highly integrated cytoskeletal and cell wall systems. Microtubules and actin filaments locally define the material properties of a tough outer cell wall to generate complex shapes. Forward genetics, powerful live cell imaging experiments, and computational modeling have provided insights into understanding of mechanisms of cell shape control. In particular, finite element modeling of the cell wall provides a new way to discover which cell wall heterogeneities generate complex cell shapes, and how cell shape and cell wall stress can feedback on the cytoskeleton to maintain growth patterns. This review focuses on cytoskeleton-dependent cell wall patterning during cell branching, and how combinations of multi-scale imaging experiments and computational modeling are being used to unravel systems-level control of morphogenesis.

Proteomic Profiling of Microtubule Self-organization in M-phase

Microtubules (MTs) and associated proteins can self-organize into complex structures such as the bipolar spindle, a process in which RanGTP plays a major role. Addition of RanGTP to M-phase Xenopus egg extracts promotes the nucleation and self-organization of MTs into asters and bipolar-like structures in the absence of centrosomes or chromosomes. We show here that the complex proteome of these RanGTP-induced MT assemblies is similar to that of mitotic spindles. Using proteomic profiling we show that MT self-organization in the M-phase cytoplasm involves the non-linear and non-stoichiometric recruitment of proteins from specific functional groups. Our study provides for the first time a temporal understanding of the protein dynamics driving MT self-organization in M-phase.

The role of the cytoskeleton in sensing changes in gravity by nonspecialized cells

A large body of evidence indicates that single cells in vitro respond to changes in gravity, and that this response might play an important role for physiological changes at the organism level during spaceflight. Gravity can lead to changes in cell proliferation, differentiation, signaling, and gene expression. At first glance, gravitational forces seem too small to affect bodies with the size of a cell. Thus, the initial response to gravity is both puzzling and important for understanding physiological changes in space. This also offers a unique environment to study the mechanical response of cells. In the past 2 decades, important steps have been made in the field of mechanobiology, and we use these advances to reevaluate the response of single cells to changes in gravity. Recent studies have focused on the cytoskeleton as initial gravity sensor. Thus, we review the observed changes in the cytoskeleton in a microgravity environment, both during spaceflight and in ground-based simulation techniques. We also evaluate to what degree the current experimental evidence supports the cytoskeleton as primary gravity sensor. Finally, we consider how the cytoskeleton itself could be affected by changed gravity. To make the next step toward understanding the response of cells to altered gravity, the challenge will be to track changes quantitatively and on short timescales.

Spinodal decomposition and the emergence of dissipative transient periodic spatio-temporal patterns in acentrosomal microtubule multitudes of different morphology

We have studied a spontaneous self-organization dynamics in a closed, dissipative (in terms of guansine 5'-triphosphate energy dissipation), reaction-diffusion system of acentrosomal microtubules (those nucleated and organized in the absence of a microtubule-organizing centre) multitude constituted of straight and curved acentrosomal microtubules, in highly crowded conditions, in vitro. Our data give experimental evidence that cross-diffusion in conjunction with excluded volume is the underlying mechanism on basis of which acentrosomal microtubule multitudes of different morphologies (straight and curved) undergo a spatial-temporal demix. Demix is constituted of a bifurcation process, manifested as a slow isothermal spinodal decomposition, and a dissipative process of transient periodic spatio-temporal pattern formation. While spinodal decomposition is an energy independent process, transient periodic spatio-temporal pattern formation is accompanied by energy dissipative process. Accordingly, we have determined that the critical threshold for slow, isothermal spinodal decomposition is 1.0 ± 0.05 mg/ml of microtubule protein concentration. We also found that periodic spacing of transient periodic spatio-temporal patterns was, in the overall, increasing versus time. For illustration, we found that a periodic spacing of the same pattern was 0.375 ± 0.036 mm, at 36 °C, at 155th min, while it was 0.540 ± 0.041 mm at 31 °C, and at 275th min after microtubule assembly started. The lifetime of transient periodic spatio-temporal patterns spans from half an hour to two hours approximately. The emergence of conditions of macroscopic symmetry breaking (that occur due to cross-diffusion in conjunction with excluded volume) may have more general but critical importance in morphological pattern development in complex, dissipative, but open cellular systems.

Directed cytoskeleton self-organization

The cytoskeleton architecture supports many cellular functions. Cytoskeleton networks form complex intracellular structures that vary during the cell cycle and between different cell types according to their physiological role. These structures do not emerge spontaneously. They result from the interplay between intrinsic self-organization properties and the conditions imposed by spatial boundaries. Along these boundaries, cytoskeleton filaments are anchored, repulsed, aligned, or reoriented. Such local effects can propagate alterations throughout the network and guide cytoskeleton assembly over relatively large distances. The experimental manipulation of spatial boundaries using microfabrication methods has revealed the underlying physical processes directing cytoskeleton self-organization. Here we review, step-by-step, from molecules to tissues, how the rules that govern assembly have been identified. We describe how complementary approaches, all based on controlling geometric conditions, from in vitro reconstruction to in vivo observation, shed new light on these fundamental organizing principles.

Hierarchical self-assembly of actin in micro-confinements using microfluidics

We present a straightforward microfluidics system to achieve step-by-step reaction sequences in a diffusion-controlled manner in quasi two-dimensional micro-confinements. We demonstrate the hierarchical self-organization of actin (actin monomers-entangled networks of filaments-networks of bundles) in a reversible fashion by tuning the [Formula: see text] ion concentration in the system. We show that actin can form networks of bundles in the presence of [Formula: see text] without any cross-linking proteins. The properties of these networks are influenced by the confinement geometry. In square microchambers we predominantly find rectangular networks, whereas triangular meshes are predominantly found in circular chambers.

Macroscopic simulations of microtubule dynamics predict two steady-state processes governing array morphology

Microtubule polymers typically function through their collective organization into a patterned array. The formation of the pattern, whether it is a relatively simple astral array or a highly complex mitotic spindle, relies on controlled microtubule nucleation and the basal dynamics parameters governing polymer growth and shortening. We have investigated the interaction between the microtubule nucleation and dynamics parameters, using macroscopic Monte Carlo simulations, to determine how these parameters contribute to the underlying microtubule array morphology (i.e. polymer density and length distribution). In addition to the well-characterized steady state achieved between free tubulin subunits and microtubule polymer, we propose that microtubule nucleation and extinction constitute a second, interdependent steady state process. Our simulation studies show that the magnitude of both nucleation and extinction additively impacts the final steady state free subunit concentration. We systematically varied individual microtubule dynamics parameters to survey the effects on array morphology and find specific sensitivity to perturbations of catastrophe frequency. Altering the cellular context for the microtubule array, we find that nucleation template number plays a defining role in shaping the microtubule length distribution and polymer density.

Cell flow reorients the axis of planar polarity in the wing epithelium of Drosophila

Planar cell polarity (PCP) proteins form polarized cortical domains that govern polarity of external structures such as hairs and cilia in both vertebrate and invertebrate epithelia. The mechanisms that globally orient planar polarity are not understood, and are investigated here in the Drosophila wing using a combination of experiment and theory. Planar polarity arises during growth and PCP domains are initially oriented toward the well-characterized organizer regions that control growth and patterning. At pupal stages, the wing hinge contracts, subjecting wing-blade epithelial cells to anisotropic tension in the proximal-distal axis. This results in precise patterns of oriented cell elongation, cell rearrangement and cell division that elongate the blade proximo-distally and realign planar polarity with the proximal-distal axis. Mutation of the atypical Cadherin Dachsous perturbs the global polarity pattern by altering epithelial dynamics. This mechanism utilizes the cellular movements that sculpt tissues to align planar polarity with tissue shape.

Plasma membrane tubulin

The association of tubulin with the plasma membrane comprises multiple levels of penetration into the bilayer: from integral membrane protein, to attachment via palmitoylation, to surface binding, and to microtubules attached by linker proteins to proteins in the membrane. Here we discuss the soundness and weaknesses of the chemical and biochemical evidence marshaled to support these associations, as well as the mechanisms by which tubulin or microtubules may regulate functions at the plasma membrane.

Collision induced spatial organization of microtubules

The dynamic behavior of microtubules in solution can be strongly modified by interactions with walls or other structures. We examine here a microtubule growth model where the increase in size of the plus-end is perturbed by collisions with other microtubules. We show that such a simple mechanism of constrained growth can induce ordered structures and patterns from an initially isotropic and homogeneous suspension. We find that microtubules self-organize locally in randomly oriented domains that grow and compete with each other. A weak orientation bias, similar to the one induced by gravity or cellular boundaries is enough to influence the domain growth direction, eventually leading to a macroscopic sample orientation.

Microtubules viewed as molecular ant colonies

Populations of ants and other social insects self-organize and develop 'emergent' properties through stigmergy in which individual ants communicate with one another via chemical trails of pheromones that attract or repulse other ants. In this way, sophisticated properties and functions develop. Under appropriate conditions, in vitro microtubule preparations, initially comprised of only tubulin and GTP, behave in a similar manner. They self-organize and develop other higher-level emergent phenomena by a process where individual microtubules are coupled together by the chemical trails they produce by their own reactive growing and shrinking. This behaviour is described and compared with the behaviour of ant colonies. Viewing microtubules as populations of molecular ants may provide new insights as to how the cytoskeleton may spontaneously develop high-level functions. It is plausible that such processes occur during the early stages of embryogenesis and in cells.

Effect of weightlessness on colloidal particle transport and segregation in self-organising microtubule preparations

Weightlessness is known to effect cellular functions by as yet undetermined processes. Many experiments indicate a role of the cytoskeleton and microtubules. Under appropriate conditions in vitro microtubule preparations behave as a complex system that self-organises by a combination of reaction and diffusion. This process also results in the collective transport and organisation of any colloidal particles present. In large centimetre-sized samples, self-organisation does not occur when samples are exposed to a brief early period of weightlessness. Here, we report both space-flight and ground-based (clinorotation) experiments on the effect of weightlessness on the transport and segregation of colloidal particles and chromosomes. In centimetre-sized containers, both methods show that a brief initial period of weightlessness strongly inhibits particle transport. In miniature cell-sized containers under normal gravity conditions, the particle transport that self-organisation causes results in their accumulation into segregated regions of high and low particle density. The gravity dependence of this behaviour is strongly shape dependent. In square wells, neither self-organisation nor particle transport and segregation occur under conditions of weightlessness. On the contrary, in rectangular canals, both phenomena are largely unaffected by weightlessness. These observations suggest, depending on factors such as cell and embryo shape, that major biological functions associated with microtubule driven particle transport and organisation might be strongly perturbed by weightlessness.

Ground-based methods reproduce space-flight experiments and show that weak vibrations trigger microtubule self-organisation

The effect of weightlessness on physical and biological systems is frequently studied by experiments in space. However, on the ground, gravity effects may also be strongly attenuated using methods such as magnetic levitation and clinorotation. Under suitable conditions, in vitro preparations of microtubules, a major element of the cytoskeleton, self-organise by a process of reaction-diffusion: self-organisation is triggered by gravity and samples prepared in space do not self-organise. Here, we report experiments carried out with ground-based methods of clinorotation and magnetic levitation. The behaviour observed closely resembles that of the space-flight experiment and suggests that many space experiments could be carried out equally well on the ground. Using clinorotation, we find that weak vibrations also trigger microtubule self-organisation and have an effect similar to gravity. Thus, in some in vitro biological systems, vibrations are a countermeasure to weightlessness.