Physical model of cellular symmetry breaking

Synthetic control of actin polymerization and symmetry breaking in active protocells

Nonlinear biomolecular interactions on membranes drive membrane remodeling crucial for biological processes including chemotaxis, cytokinesis, and endocytosis. The complexity of biomolecular interactions, their redundancy, and the importance of spatiotemporal context in membrane organization impede understanding of the physical principles governing membrane mechanics. Developing a minimal in vitro system that mimics molecular signaling and membrane remodeling while maintaining physiological fidelity poses a major challenge. Inspired by chemotaxis, we reconstructed chemically regulated actin polymerization inside vesicles, guiding membrane self-organization. An external, undirected chemical input induced directed actin polymerization and membrane deformation uncorrelated with upstream biochemical cues, suggesting symmetry breaking. A biophysical model incorporating actin dynamics and membrane mechanics proposes that uneven actin distributions cause nonlinear membrane deformations, consistent with experimental findings. This protocellular system illuminates the interplay between actin dynamics and membrane shape during symmetry breaking, offering insights into chemotaxis and other cell biological processes.

Cytoskeletal symmetry breaking in animal cells

Symmetry breaking is a crucial step in structure formation and function of all cells, necessary for cell movement, cell division, and polarity establishment. Although the mechanisms of symmetry breaking are diverse, they often share common characteristics. Here we review examples of nematic, polar, and chiral cytoskeletal symmetry breaking in animal cells, and analogous processes in simplified reconstituted systems. We discuss the origins of symmetry breaking, which can arise spontaneously, or involve amplification of a pre-existing external or internal bias to the whole cell level. The underlying mechanisms often involve both chemical and mechanical processes that cooperate to break symmetry in a robust manner, and typically depend on the shape, size, or properties of the cell's boundary.

Artificial Symmetry-Breaking for Morphogenetic Engineering Bacterial Colonies

Morphogenetic engineering is an emerging field that explores the design and implementation of self-organized patterns, morphologies, and architectures in systems composed of multiple agents such as cells and swarm robots. Synthetic biology, on the other hand, aims to develop tools and formalisms that increase reproducibility, tractability, and efficiency in the engineering of biological systems. We seek to apply synthetic biology approaches to the engineering of morphologies in multicellular systems. Here, we describe the engineering of two mechanisms, symmetry-breaking and domain-specific cell regulation, as elementary functions for the prototyping of morphogenetic instructions in bacterial colonies. The former represents an artificial patterning mechanism based on plasmid segregation while the latter plays the role of artificial cell differentiation by spatial colocalization of ubiquitous and segregated components. This separation of patterning from actuation facilitates the design-build-test-improve engineering cycle. We created computational modules for CellModeller representing these basic functions and used it to guide the design process and explore the design space in silico. We applied these tools to encode spatially structured functions such as metabolic complementation, RNAPT7 gene expression, and CRISPRi/Cas9 regulation. Finally, as a proof of concept, we used CRISPRi/Cas technology to regulate cell growth by controlling methionine synthesis. These mechanisms start from single cells enabling the study of morphogenetic principles and the engineering of novel population scale structures from the bottom up.

Balance between cell-substrate adhesion and myosin contraction determines the frequency of motility initiation in fish keratocytes

Cells are dynamic systems capable of spontaneously switching among stable states. One striking example of this is spontaneous symmetry breaking and motility initiation in fish epithelial keratocytes. Although the biochemical and mechanical mechanisms that control steady-state migration in these cells have been well characterized, the mechanisms underlying symmetry breaking are less well understood. In this work, we have combined experimental manipulations of cell-substrate adhesion strength and myosin activity, traction force measurements, and mathematical modeling to develop a comprehensive mechanical model for symmetry breaking and motility initiation in fish epithelial keratocytes. Our results suggest that stochastic fluctuations in adhesion strength and myosin localization drive actin network flow rates in the prospective cell rear above a critical threshold. Above this threshold, high actin flow rates induce a nonlinear switch in adhesion strength, locally switching adhesions from gripping to slipping and further accelerating actin flow in the prospective cell rear, resulting in rear retraction and motility initiation. We further show, both experimentally and with model simulations, that the global levels of adhesion strength and myosin activity control the stability of the stationary state: The frequency of symmetry breaking decreases with increasing adhesion strength and increases with increasing myosin contraction. Thus, the relative strengths of two opposing mechanical forces--contractility and cell-substrate adhesion--determine the likelihood of spontaneous symmetry breaking and motility initiation.

Polarization of cells and soft objects driven by mechanical interactions: consequences for migration and chemotaxis

We study a generic model for the polarization and motility of self-propelled soft objects, biological cells, or biomimetic systems, interacting with a viscous substrate. The active forces generated by the cell on the substrate are modeled by means of oscillating force multipoles at the cell-substrate interface. Symmetry breaking and cell polarization for a range of cell sizes naturally "emerge" from long range mechanical interactions between oscillating units, mediated both by the intracellular medium and the substrate. However, the harnessing of cell polarization for motility requires substrate-mediated interactions. Motility can be optimized by adapting the oscillation frequency to the relaxation time of the system or when the substrate and cell viscosities match. Cellular noise can destroy mechanical coordination between force-generating elements within the cell, resulting in sudden changes of polarization. The persistence of the cell's motion is found to depend on the cell size and the substrate viscosity. Within such a model, chemotactic guidance of cell motion is obtained by directionally modulating the persistence of motion, rather than by modulating the instantaneous cell velocity, in a way that resembles the run and tumble chemotaxis of bacteria.

Scared stiff: Stabilizing the actin cytoskeleton to stop invading cancer cells in their tracks

In recent years the concept of plasticity between invasion modes used by individual cancer cells has been gaining increasing interest in the field. Individually invading tumour cells can be divided into those that use a mesenchymal invasion mode, those that use "amoeboid" invasion and those that can switch between the two modes. The morphological distinctions between these different modes of invasion suggest that the actin cytoskeleton is likely to be a major contributor to the plasticity of cancer cell invasion mechanisms. We have recently investigated this idea by manipulating expression of Tm5NM1, one isoform of the tropomyosin family of actin-associating proteins. In a novel finding, we discovered that stabilizing the actin cytoskeleton via elevated expression of Tm5NM1 specifically inhibits mesenchymal-type cancer cell invasion, without causing transition to "amoeboid" motility-thus stopping the invading cancer cells in their tracks. The present perspective discusses our recent data in the context of current understanding of invasion plasticity and considers how stabilizing actin filaments may inhibit the mesenchymal invasion mode.

Symmetry breaking in reconstituted actin cortices

The actin cortex plays a pivotal role in cell division, in generating and maintaining cell polarity and in motility. In all these contexts, the cortical network has to break symmetry to generate polar cytoskeletal dynamics. Despite extensive research, the mechanisms responsible for regulating cortical dynamics in vivo and inducing symmetry breaking are still unclear. Here we introduce a reconstituted system that self-organizes into dynamic actin cortices at the inner interface of water-in-oil emulsions. This artificial system undergoes spontaneous symmetry breaking, driven by myosin-induced cortical actin flows, which appears remarkably similar to the initial polarization of the embryo in many species. Our in vitro model system recapitulates the rich dynamics of actin cortices in vivo, revealing the basic biophysical and biochemical requirements for cortex formation and symmetry breaking. Moreover, this synthetic system paves the way for further exploration of artificial cells towards the realization of minimal model systems that can move and divide.

DOI:http://dx.doi.org/10.7554/eLife.01433.001

Cells are extremely complex because they have to perform a vast number of processes. However, this also makes it difficult for researchers to figure out how the individual parts of the cell work. There is interest, therefore, in developing simple artificial cells that can accurately mimic how specific parts of a cell behave.

An important process for a cell is called polarization. This is where the contents of the cell arrange themselves in a way that is not symmetrical. Polarization is necessary for many cellular functions, and is particularly important during embryonic development where it helps to form the complex shape of the developing embryo.

The cytoskeleton—a dynamic structure that supports the cell and enables it to move—is crucial for polarization. An important part of the cytoskeleton is the actin cortex. This is a thin active sheet made up of a network of tiny filaments of a protein called actin that assembles at the inner face of the cell membrane. Many aspects of the structure and behavior of the actin cortex are not understood.

Abu Shah and Keren have now developed an artificial cell system using aqueous droplets surrounded by oil that can reproduce the behavior of actin cortices in real cells. An actin cortex forms upon the localization of specific nucleation factors at the inner surface of the droplets.

The artificial cortices are capable of spontaneous symmetry breaking, similar to the initial polarization in embryonic cells during development. This symmetry breaking is driven by molecular motors called myosins and depends on the connectivity of the actin network in the cortex. Experiments on the artificial cells also rule out several other mechanisms that have been proposed to explain symmetry breaking.

The work of Abu Shah and Keren represents a further step towards the goal of creating simple artificial cells that can move and divide.

DOI:http://dx.doi.org/10.7554/eLife.01433.002

Systems biology and the integration of mechanistic explanation and mathematical explanation

The paper discusses how systems biology is working toward complex accounts that integrate explanation in terms of mechanisms and explanation by mathematical models-which some philosophers have viewed as rival models of explanation. Systems biology is an integrative approach, and it strongly relies on mathematical modeling. Philosophical accounts of mechanisms capture integrative in the sense of multilevel and multifield explanations, yet accounts of mechanistic explanation (as the analysis of a whole in terms of its structural parts and their qualitative interactions) have failed to address how a mathematical model could contribute to such explanations. I discuss how mathematical equations can be explanatorily relevant. Several cases from systems biology are discussed to illustrate the interplay between mechanistic research and mathematical modeling, and I point to questions about qualitative phenomena (rather than the explanation of quantitative details), where quantitative models are still indispensable to the explanation. Systems biology shows that a broader philosophical conception of mechanisms is needed, which takes into account functional-dynamical aspects, interaction in complex networks with feedback loops, system-wide functional properties such as distributed functionality and robustness, and a mechanism's ability to respond to perturbations (beyond its actual operation). I offer general conclusions for philosophical accounts of explanation.

Cellular polarization: interaction between extrinsic bounded noises and the wave-pinning mechanism

Cell polarization (cued or uncued) is a fundamental mechanism in cell biology. As an alternative to the classical Turing bifurcation, it has been proposed that the onset of cell polarity might arise by means of the well-known phenomenon of wave-pinning [Gamba et al., Proc. Natl. Acad. Sci. USA 102, 16927 (2005)]. A particularly simple and elegant deterministic model of cell polarization based on the wave-pinning mechanism has been proposed by Edelstein-Keshet and coworkers [Biophys. J. 94, 3684 (2008)]. This model consists of a small biomolecular network where an active membrane-bound factor interconverts into its inactive form that freely diffuses in the cell cytosol. However, biomolecular networks do communicate with other networks as well as with the external world. Thus, their dynamics must be considered as perturbed by extrinsic noises. These noises may have both a spatial and a temporal correlation, and in any case they must be bounded to preserve the biological meaningfulness of the perturbed parameters. Here we numerically show that the inclusion of external spatiotemporal bounded parametric perturbations in the above wave-pinning-based model of cellular polarization may sometimes destroy the polarized state. The polarization loss depends on both the extent of temporal and spatial correlations and on the kind of noise employed. For example, an increase of the spatial correlation of the noise induces an increase of the probability of cell polarization. However, if the noise is spatially homogeneous then the polarization is lost in the majority of cases. These phenomena are independent of the type of noise. Conversely, an increase of the temporal autocorrelation of the noise induces an effect that depends on the model of noise.

Reconstruction of active regular motion in amoeba extract: dynamic cooperation between sol and gel states

Amoeboid locomotion is one of the typical modes of biological cell migration. Cytoplasmic sol–gel conversion of an actomyosin system is thought to play an important role in locomotion. However, the mechanisms underlying sol–gel conversion, including trigger, signal, and regulating factors, remain unclear. We developed a novel model system in which an actomyosin fraction moves like an amoeba in a cytoplasmic extract. Rheological study of this model system revealed that the actomyosin fraction exhibits shear banding: the sol–gel state of actomyosin can be regulated by shear rate or mechanical force. Furthermore, study of the living cell indicated that the shear-banding property also causes sol–gel conversion with the same order of magnitude as that of shear rate. Our results suggest that the inherent sol–gel transition property plays an essential role in the self-regulation of autonomous translational motion in amoeba.

Asymmetric ligand binding facilitates conformational transitions in pentameric ligand-gated ion channels

The anesthetic propofol inhibits the currents of the homopentameric ligand-gated ion channel GLIC, yet the crystal structure of GLIC with five propofol molecules bound symmetrically shows an open-channel conformation. To address this dilemma and determine if the symmetry of propofol binding sites affects the channel conformational transition, we performed a total of 1.5 μs of molecular dynamics simulations for different GLIC systems with propofol occupancies of 0, 1, 2, 3, and 5. GLIC without propofol binding or with five propofol molecules bound symmetrically, showed similar channel conformation and hydration status over multiple replicates of 100-ns simulations. In contrast, asymmetric binding to one, two or three equivalent sites in different subunits accelerated the channel dehydration, increased the conformational heterogeneity of the pore-lining TM2 helices, and shifted the lateral and radial tilting angles of TM2 toward a closed-channel conformation. The results differentiate two groups of systems based on the propofol binding symmetry. The difference between symmetric and asymmetric groups is correlated with the variance in the propofol-binding cavity adjacent to the hydrophobic gate and the force imposed by the bound propofol. Asymmetrically bound propofol produced greater variance in the cavity size that could further elevate the conformation heterogeneity. The force trajectory generated by propofol in each subunit over the course of a simulation exhibits an ellipsoidal shape, which has the larger component tangential to the pore. Asymmetric propofol binding creates an unbalanced force that expedites the channel conformation transitions. The findings from this study not only suggest that asymmetric binding underlies the propofol functional inhibition of GLIC, but also advocate for the role of symmetry breaking in facilitating channel conformational transitions.

Cell polarity: quantitative modeling as a tool in cell biology

Among a number of innovative approaches that have modernized cell biology, modeling has a prominent yet unusual place. One popular view is that we progress linearly, from conceptual to ever more detailed models. We review recent discoveries of cell polarity mechanisms, in which modeling played an important role, to demonstrate that the experiment-theory feedback loop requires diverse models characterized by varying levels of biological detail and mathematical complexity. We argue that a quantitative model is a tool that has to fit an experimental study, and the model's value should be judged not by how complex and detailed it is, but by what could be learned from it.

Weakly nonlinear analysis of symmetry breaking in cell polarity models

Spontaneous symmetry breaking leading to polarization of the cell is a key step initiating many morphogenetic processes. In addition to experimental studies, model-based theoretical description helps to understand the conditions and limitations of this process. Such description is limited usually to linear stability analysis supplied by the numerical simulations to establish the dependence of the polarization dynamics on the model parameters. Here we describe the application of a powerful weakly nonlinear analysis method to a minimalistic model characterized by the conservation of mass of the protein governing the polarization dynamics.

Cellular symmetry breaking during Caenorhabditis elegans development

The nematode worm Caenorhabditis elegans has produced a wellspring of insights into mechanisms that govern cellular symmetry breaking during animal development. Here we focus on two highly conserved systems that underlie many of the key symmetry-breaking events that occur during embryonic and larval development in the worm. One involves the interplay between Par proteins, Rho GTPases, and the actomyosin cytoskeleton and mediates asymmetric cell divisions that establish the germline. The other uses elements of the Wnt signaling pathway and a highly reiterative mechanism that distinguishes anterior from posterior daughter cell fates. Much of what we know about these systems comes from intensive study of a few key events-Par/Rho/actomyosin-mediated polarization of the zygote in response to a sperm-derived cue and the Wnt-mediated induction of endoderm at the four-cell stage. However, a growing body of work is revealing how C. elegans exploits elements/variants of these systems to accomplish a diversity of symmetry-breaking tasks throughout embryonic and larval development.

Symmetry breaking in biology

Symmetry breaking is essential for cell movement, polarity, and developmental patterning. Amplification of initial asymmetry is key to the conserved mechanisms involved.

Cytoskeletal mechanisms for breaking cellular symmetry

Cytoskeletal systems are networks of polymers found in all eukaryotic and many prokaryotic cells. Their purpose is to transmit and integrate information across cellular dimensions and help turn a disorderly mob of macromolecules into a spatially organized, living cell. Information, in this context, includes physical and chemical properties relevant to cellular physiology, including: the number and activity of macromolecules, cell shape, and mechanical force. Most animal cells are 10-50 microns in diameter, whereas the macromolecules that comprise them are 10,000-fold smaller (2-20 nm). To establish long-range order over cellular length scales, individual molecules must, therefore, self-assemble into larger polymers, with lengths (0.1-20 m) comparable to the size of a cell. These polymers must then be cross-linked into organized networks that fill the cytoplasm. Such cell-spanning polymer networks enable different parts of the cytoplasm to communicate directly with each other, either by transmitting forces or by carrying cargo from one spot to another.