Lipid membranes supported by polydimethylsiloxane substrates with designed geometry.

The membrane curvature of cells and intracellular compartments continuously adapts to enable cells to perform vital functions, from cell division to signal trafficking. Understanding how membrane geometry affects these processes in vivo is challenging because of the biochemical and geometrical complexity as well as the short time and small length scales involved in cellular processes. By contrast, in vitro model membranes with engineered curvature would provide a versatile platform for this investigation and applications to biosensing and biocomputing. Here, we present a strategy that allows fabrication of lipid membranes with designed shape by combining 3D micro-printing and replica-molding lithography with polydimethylsiloxane to create curved micrometer-sized scaffolds with virtually any geometry. The resulting supported lipid membranes are homogeneous and fluid. We demonstrate the versatility of the system by fabricating structures of interesting combinations of mean and Gaussian curvature. We study the lateral phase separation and how local curvature influences the effective diffusion coefficient. Overall, we offer a bio-compatible platform for understanding curvature-dependent cellular processes and developing programmable bio-interfaces for living cells and nanostructures.

Lipid exchange enhances geometric pinning in multicomponent membranes on patterned substrates.

Experiments on supported lipid bilayers featuring liquid ordered/disordered domains have shown that the spatial arrangement of the lipid domains and their chemical composition are strongly affected by the curvature of the substrate. Furthermore, theoretical predictions suggest that both these effects are intimately related with the closed topology of the bilayer. In this work, we test this hypothesis by fabricating supported membranes consisting of colloidal particles of various shapes lying on a flat substrate. A single lipid bilayer coats both colloids and substrate, allowing local lipid exchange between them, thus rendering the system thermodynamically open, i.e. able to exchange heat and molecules with an external reservoir in the neighborhood of the colloid. By reconstructing the Gibbs phase diagram for this system, we demonstrate that the free-energy landscape is directly influenced by the geometry of the colloid. In addition, we find that local lipid exchange enhances the pinning of the liquid disordered phase in highly curved regions. This allows us to provide estimates of the bending moduli difference of the domains. Finally, by combining experimental and numerical data, we forecast the outcome of possible experiments on catenoidal and conical necks and show that these geometries could greatly improve the precision of the current estimates of the bending moduli.

Colloid supported lipid bilayers for self-assembly.

The use of colloid supported lipid bilayers (CSLBs) has recently been extended to create colloidal joints, that enable the assembly of structures with internal degrees of flexibility, and to study lipid membranes on curved and closed geometries. These novel applications of CSLBs rely on previously unappreciated properties: the simultaneous fluidity of the bilayer, lateral mobility of inserted (linker) molecules and colloidal stability. Here we characterize every step in the manufacturing of CSLBs in view of these requirements using confocal microscopy and fluorescence recovery after photobleaching (FRAP). Specifically, we have studied the influence of different particle properties (roughness, surface charge, chemical composition, polymer coating) on the quality and mobility of the supported bilayer. We find that the insertion of lipopolymers in the bilayer can affect its homogeneity and fluidity. We improve the colloidal stability by inserting lipopolymers or double-stranded inert DNA into the bilayer. We include surface-mobile DNA linkers and use FRAP to characterize their lateral mobility both in their freely diffusive and bonded state. Finally, we demonstrate the self-assembly of flexibly linked structures from the CSLBs modified with surface-mobile DNA linkers. Our work offers a collection of experimental tools for working with CSLBs in applications ranging from controlled bottom-up self-assembly to model membrane studies.

The cell cycle oscillator and spindle length set the speed of chromosome separation in Drosophila embryos.

Anaphase is tightly controlled in space and time to ensure proper separation of chromosomes. The mitotic spindle, the self-organized microtubule structure driving chromosome segregation, scales in size with the available cytoplasm. Yet, the relationship between spindle size and chromosome movement remains poorly understood. Here, we address how the movement of chromosomes changes during the cleavage divisions of the Drosophila blastoderm. We show that the speed of chromosome separation gradually decreases during the 4 nuclear divisions of the blastoderm. This reduction in speed is accompanied by a similar reduction in the length of the spindle, thus ensuring that these two quantities are tightly linked. Using a combination of genetic and quantitative imaging approaches, we find that two processes contribute to controlling the speed at which chromosomes move at mitotic exit: the activity of molecular motors important for microtubule depolymerization and the cell cycle oscillator. Specifically, we found that the levels of Klp10A, Klp67A, and Klp59C, three kinesin-like proteins important for microtubule depolymerization, contribute to setting the speed of chromosome separation. This observation is supported by quantification of microtubule dynamics indicating that poleward flux rate scales with the length of the spindle. Perturbations of the cell cycle oscillator using heterozygous mutants of mitotic kinases and phosphatases revealed that the duration of anaphase increases during the blastoderm cycles and is the major regulator of chromosome velocity. Thus, our work suggests a potential link between the biochemical rate of mitotic exit and the forces exerted by the spindle. Collectively, we propose that the cell cycle oscillator and spindle length set the speed of chromosome separation in anaphase.

Robust cytoplasmic partitioning by solving an intrinsic cytoskeletal instability.

Early development across vertebrates and insects critically relies on robustly reorganizing the cytoplasm of fertilized eggs into individualized cells. This intricate process is orchestrated by large microtubule structures that traverse the embryo, partitioning the cytoplasm into physically distinct and stable compartments. Despite the robustness of embryonic development, here we uncover an intrinsic instability in cytoplasmic partitioning driven by the microtubule cytoskeleton. We reveal that embryos circumvent this instability through two distinct mechanisms: either by matching the cell cycle duration to the time needed for the instability to unfold or by limiting microtubule nucleation. These regulatory mechanisms give rise to two possible strategies to fill the cytoplasm, which we experimentally demonstrate in zebrafish and Drosophila embryos, respectively. In zebrafish embryos, unstable microtubule waves fill the geometry of the entire embryo from the first division. Conversely, in Drosophila embryos, stable microtubule asters resulting from reduced microtubule nucleation gradually fill the cytoplasm throughout multiple divisions. Our results indicate that the temporal control of microtubule dynamics could have driven the evolutionary emergence of species-specific mechanisms for effective cytoplasmic organization. Furthermore, our study unveils a fundamental synergy between physical instabilities and biological clocks, uncovering universal strategies for rapid, robust, and efficient spatial ordering in biological systems.

Activity-induced interactions and cooperation of artificial microswimmers in one-dimensional environments.

Cooperative motion in biological microswimmers is crucial for their survival as it facilitates adhesion to surfaces, formation of hierarchical colonies, efficient motion, and enhanced access to nutrients. Here, we confine synthetic, catalytic microswimmers along one-dimensional paths and demonstrate that they too show a variety of cooperative behaviours. We find that their speed increases with the number of swimmers, and that the activity induces a preferred distance between swimmers. Using a minimal model, we ascribe this behavior to an effective activity-induced potential that stems from a competition between chemical and hydrodynamic coupling. These interactions further induce active self-assembly into trains where swimmers move at a well-separated, stable distance with respect to each other, as well as compact chains that can elongate, break-up, become immobilized and remobilized. We identify the crucial role that environment morphology and swimmer directionality play on these highly dynamic chain behaviors. These activity-induced interactions open the door toward exploiting cooperation for increasing the efficiency of microswimmer motion, with temporal and spatial control, thereby enabling them to perform intricate tasks inside complex environments.

Geometric pinning and antimixing in scaffolded lipid vesicles.

Previous studies on the phase behaviour of multicomponent lipid bilayers found an intricate interplay between membrane geometry and its composition, but a fundamental understanding of curvature-induced effects remains elusive. Thanks to a combination of experiments on lipid vesicles supported by colloidal scaffolds and theoretical work, we demonstrate that the local geometry and global chemical composition of the bilayer determine both the spatial arrangement and the amount of mixing of the lipids. In the mixed phase, a strong geometrical anisotropy can give rise to an antimixed state, where the lipids are mixed, but their relative concentration varies across the membrane. After phase separation, the bilayer organizes in multiple lipid domains, whose location is pinned in specific regions, depending on the substrate curvature and the bending rigidity of the lipid domains. Our results provide critical insights into the phase separation of cellular membranes and, more generally, two-dimensional fluids on curved substrates.

Thermodynamic equilibrium of binary mixtures on curved surfaces.

We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and conservation laws, we identify several model-independent phenomena, such as a curvature-dependent line tension and local shifts in the binodal concentrations. To shed light on the origin of the phenomenological parameters appearing in the effective free energy, we further construct a lattice-gas model of binary mixtures on nontrivial substrates, based on the curved-space generalization of the two-dimensional Ising model. This allows us to decompose the interaction between the local concentration of the mixture and the substrate curvature into four distinct contributions, as a result of which the phase diagram splits into critical subdiagrams. The resulting free energy landscape can admit, as stable equilibria, strongly inhomogeneous mixed phases, which we refer to as "antimixed" states below the critical temperature. We corroborate our semianalytical findings with phase-field numerical simulations on realistic curved lattices. Despite this work being primarily motivated by recent experimental observations of multicomponent lipid vesicles supported by colloidal scaffolds, our results are applicable to any binary mixture confined on closed surfaces of arbitrary geometry.