Rhythmicity and waves in the cortex of single cells

Nonlinear dynamics in phosphoinositide metabolism

Phosphoinositides broadly impact membrane dynamics, signal transduction and cellular physiology. The orchestration of signaling complexity by this seemingly simple metabolic pathway remains an open question. It is increasingly evident that comprehending the complexity of the phosphoinositides metabolic network requires a systems view based on nonlinear dynamics, where the products of metabolism can either positively or negatively modulate enzymatic function. These feedback and feedforward loops may be paradoxical, leading to counterintuitive effects. In this review, we introduce the framework of nonlinear dynamics, emphasizing distinct dynamical regimes such as the excitable state, oscillations, and mixed-mode oscillations-all of which have been experimentally observed in phosphoinositide metabolisms. We delve into how these dynamical behaviors arise from one or multiple network motifs, including positive and negative feedback loops, coherent and incoherent feedforward loops. We explore the current understanding of the molecular circuits responsible for these behaviors. While mapping these circuits presents both conceptual and experimental challenges, redefining cellular behavior based on dynamical state, lipid fluxes, time delay, and network topology is likely essential for a comprehensive understanding of this fundamental metabolic network.

Collective dynamics of actin and microtubule and its crosstalk mediated by FHDC1

The coordination between actin and microtubule network is crucial, yet this remains a challenging problem to dissect and our understanding of the underlying mechanisms remains limited. In this study, we used travelling waves in the cell cortex to characterize the collective dynamics of cytoskeletal networks. Our findings show that Cdc42 and F-BAR-dependent actin waves in mast cells are mainly driven by formin-mediated actin polymerization, with the microtubule-binding formin FH2 domain-containing protein 1 (FHDC1) as an early regulator. Knocking down FHDC1 inhibits actin wave formation, and this inhibition require FHDC1's interaction with both microtubule and actin. The phase of microtubule depolymerization coincides with the nucleation of actin waves and microtubule stabilization inhibit actin waves, leading us to propose that microtubule shrinking and the concurrent release of FHDC1 locally regulate actin nucleation. Lastly, we show that FHDC1 is crucial for multiple cellular processes such as cell division and migration. Our data provided molecular insights into the nucleation mechanisms of actin waves and uncover an antagonistic interplay between microtubule and actin polymerization in their collective dynamics.

Disappearance, division, and route change of excitable reaction-diffusion waves in deformable membranes

Shapes of biomembrane in living cells are regulated by curvature-inducing proteins. However, the effects of membrane deformation on signal transductions such as chemical waves have not been researched adequately. Here, we report that membrane deformation can alter the propagation of excitable reaction-diffusion waves using state-of-the-art simulations. Reaction waves can induce large shape transformations, such as membrane budding and necking, that erase or divide the wave, depending on the curvature generated by the waves, feedback to the wave propagation, and the ratio of the reaction and deformation times. In genus-2 vesicles, wave division occurs at branching points and collided waves disappear together. We demonstrate that the occasional disappearance of the waves can alter the pathway of wave propagation. Our findings suggest that membrane deformation and reaction waves can together regulate signal transductions on biomembranes.

Does the Extracellular Matrix Support Cell-Cell Communication by Elastic Wave Packets?

The extracellular matrix (ECM) is a fibrous network supporting biological cells and provides them a medium for interaction. Cells modify the ECM by applying traction forces, and these forces can propagate to long ranges and establish a mechanism of mechanical communication between neighboring cells. Previous studies have mainly focused on analysis of static force transmission across the ECM. In this study, we explore the plausibility of dynamic mechanical interaction, expressed as vibrations or abrupt fluctuations, giving rise to elastic waves propagating along ECM fibers. We use a numerical mass-spring model to simulate the longitudinal and transversal waves propagating along a single ECM fiber and across a 2D random fiber network. The elastic waves are induced by an active contracting cell (signaler) and received by a passive neighboring cell (receiver). We show that dynamic wave propagation may amplify the signal at the receiver end and support up to an order of magnitude stronger mechanical cues and longer-ranged communication relative to static transmission. Also, we report an optimal impulse duration corresponding to the most effective transmission, as well as extreme fast impulses, in which the waves are encaged around the active cell and do not reach the neighboring cell, possibly due to the Anderson localization effect. Finally, we also demonstrate that extracellular fluid viscosity reduces, but still allows, dynamic propagation along embedded ECM fibers. Our results motivate future biological experiments in mechanobiology to investigate, on the one hand, the mechanosensitivity of cells to dynamic forces traveling and guided by the ECM and, on the other hand, the impact of ECM architecture and remodeling on dynamic force transmission and its spectral filtering, dispersion, and decay.

OSCILLATORS IN THE MICROVASCULATURE - GLYCOCALYX AND BEYOND

The growing recognition of abundance of oscillating functions in biological systems has motivated this brief overview which narrows down on the microvasculature. Specifically, it encompasses self-sustained oscillations of blood flow, hematocrit and viscosity at bifurcations; their effects on the oscillations of endothelial glycocalyx, mechanotransduction and its termination to prime endothelial cells for the subsequent mechanical signaling event; oscillating affinity of hyaluronan-CD44 binding domain; spontaneous contractility of actomyosin complexes in the cortical actin web, its effects on the tension of the plasma membrane; reversible effects of sirtuin-1 on endothelial glycocalyx; and effects of plasma membrane tension on endo-and exocytosis. Some potential interactions between those oscillators - their coupling - are discussed together with their transition into chaotic movements. Future in-depth understanding of the oscillatory activities in the microvasculature could serve as a guide to its chronotherapy under pathological conditions.

Cellular sentience as the primary source of biological order and evolution

All life is cellular, starting some 4 billion years ago with the emergence of the first cells. In order to survive their early evolution in the face of an extremely challenging environment, the very first cells invented cellular sentience and cognition, allowing them to make relevant decisions to survive through creative adaptations in a continuously running evolutionary narrative. We propose that the success of cellular life has crucially depended on a biological version of Maxwell's demons which permits the extraction of relevant sensory information and energy from the cellular environment, allowing cells to sustain anti-entropic actions. These sensor-effector actions allowed for the creative construction of biological order in the form of diverse organic macromolecules, including crucial polymers such as DNA, RNA, and cytoskeleton. Ordered biopolymers store analogue (structures as templates) and digital (nucleotide sequences of DNA and RNA) information that functioned as a form memory to support the development of organisms and their evolution. Crucially, all cells are formed by the division of previous cells, and their plasma membranes are physically and informationally continuous across evolution since the beginning of cellular life. It is argued that life is supported through life-specific principles which support cellular sentience, distinguishing life from non-life. Biological order, together with cellular cognition and sentience, allow the creative evolution of all living organisms as the authentic authors of evolutionary novelty.

Dynamic surface patterns on cells

Dynamic pattern formations are commonly observed in multicellular systems, such as cardiac tissue and slime molds, and modeled using reaction–diffusion systems. Recent experiments have revealed dynamic patterns in the concentration profile of various cortical proteins at a much smaller scale, namely, embryos at their single-cell stage. Spiral waves of Rho and F-actin proteins have been reported in Xenopus frog and starfish oocytes [Bement et al., Nat. Cell Biol. 17, 1471 (2015)], while a pulsatile pattern of Rho and myosin proteins has been found in C. elegans embryo [Nishikawa et al., eLife 6, e30537 (2017)]. Here, we propose that these two seemingly distinct dynamic patterns are signatures of a single reaction–diffusion network involving active-Rho, inactive-Rho, actin, and myosin. We show that a small variation in the concentration of other ancillary proteins can give rise to different dynamical states from the same chemical network.

Reaction-diffusion waves coupled with membrane curvature

The reaction-diffusion waves of proteins are known to be involved in fundamental cellular functions, such as cell migration, cell division, and vesicular transportation. In some of these phenomena, pattern formation on the membranes is induced by the coupling between membrane deformation and the reaction-diffusion system through curvature-inducing proteins that bend the biological membranes. Although the membrane shape and the dynamics of the curvature-inducing proteins affect each other in these systems, the effect of such mechanochemical feedback loops on the waves has not been studied in detail. In this study, reaction-diffusion waves coupled with membrane deformation are investigated using simulations combining a dynamically triangulated membrane model with the Brusselator model extended to include the effect of membrane curvature. It is found that the propagating wave patterns change into nonpropageting patterns and spiral wave patterns due to the mechanochemical effects. Moreover, the wave speed is positively or negatively correlated with the local membrane curvature depending on the spontaneous curvature and bending rigidity. In addition, self-oscillation of the vesicle shape occurs, associated with the reaction-diffusion waves of curvature-inducing proteins. This agrees with the experimental observation of GUVs with a reconstituted Min system, which plays a key role in the cell division of Escherichia coli. The findings of this study demonstrate the importance of mechanochemical coupling in biological phenomena.

Pinching the cortex of live cells reveals thickness instabilities caused by myosin II motors

The cell cortex is a contractile actin meshwork, which determines cell shape and is essential for cell mechanics, migration, and division. Because its thickness is below optical resolution, there is a tendency to consider the cortex as a thin uniform two-dimensional layer. Using two mutually attracted magnetic beads, one inside the cell and the other in the extracellular medium, we pinch the cortex of dendritic cells and provide an accurate and time-resolved measure of its thickness. Our observations draw a new picture of the cell cortex as a highly dynamic layer, harboring large fluctuations in its third dimension because of actomyosin contractility. We propose that the cortex dynamics might be responsible for the fast shape-changing capacity of highly contractile cells that use amoeboid-like migration.

Binding of thermalized and active membrane curvature-inducing proteins

The phase behavior of a membrane induced by the binding of curvature-inducing proteins is studied by a combination of analytical and numerical approaches. In thermal equilibrium under the detailed balance between binding and unbinding, the membrane exhibits three phases: an unbound uniform flat phase (U), a bound uniform flat phase (B), and a separated/corrugated phase (SC). In the SC phase, the bound proteins form hexagonally-ordered bowl-shaped domains. The transitions between the U and SC phases and between the B and SC phases are second order and first order, respectively. At a small spontaneous curvature of the protein or high surface tension, the transition between B and SC phases becomes continuous. Moreover, a first-order transition between the U and B phases is found at zero spontaneous curvature driven by the Casimir-like interactions between rigid proteins. Furthermore, nonequilibrium dynamics is investigated by the addition of active binding and unbinding at a constant rate. The active binding and unbinding processes alter the stability of the SC phase.

Pattern formation in reaction-diffusion system on membrane with mechanochemical feedback

Shapes of biological membranes are dynamically regulated in living cells. Although membrane shape deformation by proteins at thermal equilibrium has been extensively studied, nonequilibrium dynamics have been much less explored. Recently, chemical reaction propagation has been experimentally observed in plasma membranes. Thus, it is important to understand how the reaction-diffusion dynamics are modified on deformable curved membranes. Here, we investigated nonequilibrium pattern formation on vesicles induced by mechanochemical feedback between membrane deformation and chemical reactions, using dynamically triangulated membrane simulations combined with the Brusselator model. We found that membrane deformation changes stable patterns relative to those that occur on a non-deformable curved surface, as determined by linear stability analysis. We further found that budding and multi-spindle shapes are induced by Turing patterns, and we also observed the transition from oscillation patterns to stable spot patterns. Our results demonstrate the importance of mechanochemical feedback in pattern formation on deforming membranes.

Motion magnification analysis of microscopy videos of biological cells

It is well recognized that isolated cardiac muscle cells beat in a periodic manner. Recently, evidence indicates that other, non-muscle cells, also perform periodic motions that are either imperceptible under conventional lab microscope lens or practically not easily amenable for analysis of oscillation amplitude, frequency, phase of movement and its direction. Here, we create a real-time video analysis tool to visually magnify and explore sub-micron rhythmic movements performed by biological cells and the induced movements in their surroundings. Using this tool, we suggest that fibroblast cells perform small fluctuating movements with a dominant frequency that is dependent on their surrounding substrate and its stiffness.

Mechanobiology in cortical waves and oscillations

Cortical actin waves have emerged as a widely prevalent phenomena and brought pattern formation to many fields of cell biology. Cortical excitabilities, reminiscent of the electric excitability in neurons, are likely fundamental property of the cell cortex. Although they have been mostly considered to be biochemical in nature, accumulating evidence support the role of mechanics in the pattern formation process. Both pattern formation and mechanobiology approach biological phenomena at the collective level, either by looking at the mesoscale dynamical behavior of molecular networks or by using collective physical properties to characterize biological systems. As such they are very different from the traditional reductionist, bottom-up view of biology, which brings new challenges and potential opportunities. In this essay, we aim to provide our perspectives on what the proposed mechanochemical feedbacks are and open questions regarding their role in cortical excitable and oscillatory dynamics.

Three-dimensional organization of the cytoskeleton: A cryo-electron tomography perspective

Traditionally, structures of cytoskeletal components have been studied ex situ, that is, with biochemically purified materials. There are compelling reasons to develop approaches to study them in situ in their native functional context. In recent years, cryo-electron tomography emerged as a powerful method for visualizing the molecular organization of unperturbed cellular landscapes with the potential to attain near-atomic resolution. Here, we review recent works on the cytoskeleton using cryo-electron tomography, demonstrating the power of in situ studies. We also highlight the potential of this method in addressing important questions pertinent to the field of cytoskeletal biomechanics.

Deconstructing Actin Waves

In this issue of Structure, Jasnin et al. (2019) shows how actin waves on the ventral membrane of Dictyostelium cells propagate by de novo nucleation of oblique filaments that are polarized toward the ventral membrane without a preference to the wave direction.

The E. coli MinCDE system in the regulation of protein patterns and gradients

Molecular self-organziation, also regarded as pattern formation, is crucial for the correct distribution of cellular content. The processes leading to spatiotemporal patterns often involve a multitude of molecules interacting in complex networks, so that only very few cellular pattern-forming systems can be regarded as well understood. Due to its compositional simplicity, the Escherichia coli MinCDE system has, thus, become a paradigm for protein pattern formation. This biological reaction diffusion system spatiotemporally positions the division machinery in E. coli and is closely related to ParA-type ATPases involved in most aspects of spatiotemporal organization in bacteria. The ATPase MinD and the ATPase-activating protein MinE self-organize on the membrane as a reaction matrix. In vivo, these two proteins typically oscillate from pole-to-pole, while in vitro they can form a variety of distinct patterns. MinC is a passenger protein supposedly operating as a downstream cue of the system, coupling it to the division machinery. The MinCDE system has helped to extract not only the principles underlying intracellular patterns, but also how they are shaped by cellular boundaries. Moreover, it serves as a model to investigate how patterns can confer information through specific and non-specific interactions with other molecules. Here, we review how the three Min proteins self-organize to form patterns, their response to geometric boundaries, and how these patterns can in turn induce patterns of other molecules, focusing primarily on experimental approaches and developments.

Self-organization: the fundament of cell biology

Self-organization refers to the emergence of an overall order in time and space of a given system that results from the collective interactions of its individual components. This concept has been widely recognized as a core principle in pattern formation for multi-component systems of the physical, chemical and biological world. It can be distinguished from self-assembly by the constant input of energy required to maintain order-and self-organization therefore typically occurs in non-equilibrium or dissipative systems. Cells, with their constant energy consumption and myriads of local interactions between distinct proteins, lipids, carbohydrates and nucleic acids, represent the perfect playground for self-organization. It therefore comes as no surprise that many properties and features of self-organized systems, such as spontaneous formation of patterns, nonlinear coupling of reactions, bi-stable switches, waves and oscillations, are found in all aspects of modern cell biology. Ultimately, self-organization lies at the heart of the robustness and adaptability found in cellular and organismal organization, and hence constitutes a fundamental basis for natural selection and evolution.This article is part of the theme issue 'Self-organization in cell biology'.

Actin Cytoskeleton and Focal Adhesions Regulate the Biased Migration of Breast Cancer Cells on Nanoscale Asymmetric Sawteeth

Physical guidance from the underlying matrix is a key regulator of cancer invasion and metastasis. We explore the effects of surface topography on the migration phenotype of multiple breast cancer cell lines using aligned nanoscale ridges and asymmetric sawtooth structures. Both benign and metastatic breast cancer cells preferentially move parallel to nanoridges, with enhanced speeds compared to flat surfaces. In contrast, asymmetric sawtooth structures unidirectionally bias the movement of breast cancer cells in a cell-type-dependent manner. Quantitative analysis shows that the level of bias in cell migration increases when cells move with higher speeds or with higher directional persistence. Live-cell imaging studies further reveal that actin polymerization waves are unidirectionally guided by the sawteeth in the same direction as the cell motion. High-resolution fluorescence imaging and scanning electron microscopy studies reveal that two breast cancer cell lines with opposite migrational profiles exhibit profoundly different cell cortical plasticity and focal adhesion patterns. These results suggest that the overall migration response of cancer cells to surface topography is directly related to the underlying cytoskeletal architectures and dynamics, which are regulated by both intrinsic and extrinsic factors.