Spontaneous symmetry breaking turing-type pattern formation in a confined Dictyostelium cell mass

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.

Synthetic control of actin polymerization and symmetry breaking in active protocells

Non-linear biomolecular interactions on the membranes drive membrane remodeling that underlies fundamental biological processes including chemotaxis, cytokinesis, and endocytosis. The multitude of biomolecules, the redundancy in their interactions, and the importance of spatiotemporal context in membrane organization hampers understanding the physical principles governing membrane mechanics. A minimal, in vitro system that models the functional interactions between molecular signaling and membrane remodeling, while remaining faithful to cellular physiology and geometry is powerful yet remains unachieved. Here, inspired by the biophysical processes underpinning chemotaxis, we reconstituted externally-controlled actin polymerization inside giant unilamellar vesicles, guiding self-organization on the membrane. We show that applying undirected external chemical inputs to this system results in directed actin polymerization and membrane deformation that are uncorrelated with upstream biochemical cues, indicating symmetry breaking. A biophysical model of the dynamics and mechanics of both actin polymerization and membrane shape suggests that inhomogeneous distributions of actin generate membrane shape deformations in a non-linear fashion, a prediction consistent with experimental measurements and subsequent local perturbations. The active protocellular system demonstrates the interplay between actin dynamics and membrane shape in a symmetry breaking context that is relevant to chemotaxis and a suite of other biological processes.

Onset model of mutually catalytic self-replicative systems formed by an assembly of polynucleotides

Self-replicability is a unique attribute observed in all living organisms, and the question of how the life was physically initiated could be equivalent to the question of how self-replicating informative polymers were formed in the abiotic material world. It has been suggested that the present DNA and proteins world was preceded by an RNA world in which genetic information of RNA molecules was replicated by the mutual catalytic function of RNA molecules. However, the important question of how the transition occurred from a material world to the very early pre-RNA world remains unsolved both experimentally and theoretically. We present an onset model of mutually catalytic self-replicative systems formed in an assembly of polynucleotides. A quantitative expression of the critical condition for the onset of growing fluctuation towards self-replication in this model is obtained by analytical and numerical calculations.

Novel micropatterning technique reveals dependence of cell-substrate adhesion and migration of social amoebas on parental strain, development, and fluorescent markers

Cell-substrate adhesion of the social amoeba Dictyostelium discoideum, a model organism often used for the study of chemotaxis, is non-specific and does not involve focal adhesion complexes. Therefore, micropatterned substrates where adherent Dictyostelium cells are constrained to designated microscopic regions are difficult to make. Here we present a micropatterning technique for Dictyostelium cells that relies on coating the substrate with an ∼1μm thick layer of polyethylene glycol (PEG) gel. We show that, when plated on a substrate with narrow parallel stripes of PEG-gel and glass, Dictyostelium cells nearly exclusive adhere to and migrate along the glass stripes, thus providing a model system to study one-dimensional migration of amoeboid cells. Surprisingly, we find substantial differences in the adhesion to PEG-gel and glass stripes between vegetative and developed cells and between two different axenic laboratory strains of Dictyostelium, AX2 and AX4. Even more surprisingly, we find that the distribution of Dictyostelium cells between PEG-gel and glass stripes is significantly affected by the expression of several fluorescent protein markers of the cytoskeleton. We carry out atomic force microscopy based single cell force spectroscopy measurements that confirm that the force of adhesion to PEG-gel substrate can be significantly different between vegetative and developed cells, AX2 and AX4 cells, and cells with and without fluorescent markers. Thus, the choice of parental background, the degree of development, and the expression of fluorescent protein markers can all have a profound effect on cell-substrate adhesion and should be considered when comparing migration of cells and when designing micropatterned substrates.

Symmetry breaking dynamics induced by mean-field density and low-pass filter

The phenomenon of spontaneous symmetry breaking facilitates the onset of a plethora of nontrivial dynamical states/patterns in a wide variety of dynamical systems. Spontaneous symmetry breaking results in amplitude and phase variations in a coupled identical oscillator due to the breaking of the prevailing permutational/translational symmetry of the coupled system. Nevertheless, the role and the competing interaction of the low-pass filter and the mean-field density parameter on the symmetry breaking dynamical states are unclear and yet to be explored explicitly. The effect of low pass filtering along with the mean-field parameter is explored in conjugately coupled Stuart-Landau oscillators. The dynamical transitions are examined via bifurcation analysis. We show the emergence of a spontaneous symmetry breaking (asymmetric) oscillatory state, which coexists with a nontrivial amplitude death state. Through the basin of attraction, the multi-stable nature of the spontaneous symmetry breaking state is examined, which reveals that the asymmetric distribution of the initial state favors the spontaneous symmetry breaking dynamics, while the symmetric distribution of initial states gives rise to the nontrivial amplitude death state. In addition, the trade-off between the cut-off frequency of the low-pass filter along with the mean-field density induces and enhances the symmetry breaking dynamical states. Global dynamical transitions are discussed as a function of various system parameters. Analytical stability curves corresponding to the nontrivial amplitude death and oscillation death states are deduced.

Synchrony and pattern formation of coupled genetic oscillators on a chip of artificial cells

Understanding how biochemical networks lead to large-scale nonequilibrium self-organization and pattern formation in life is a major challenge, with important implications for the design of programmable synthetic systems. Here, we assembled cell-free genetic oscillators in a spatially distributed system of on-chip DNA compartments as artificial cells, and measured reaction-diffusion dynamics at the single-cell level up to the multicell scale. Using a cell-free gene network we programmed molecular interactions that control the frequency of oscillations, population variability, and dynamical stability. We observed frequency entrainment, synchronized oscillatory reactions and pattern formation in space, as manifestation of collective behavior. The transition to synchrony occurs as the local coupling between compartments strengthens. Spatiotemporal oscillations are induced either by a concentration gradient of a diffusible signal, or by spontaneous symmetry breaking close to a transition from oscillatory to nonoscillatory dynamics. This work offers design principles for programmable biochemical reactions with potential applications to autonomous sensing, distributed computing, and biomedical diagnostics.

Turing Patterning Using Gene Circuits with Gas-Induced Degradation of Quorum Sensing Molecules

The Turing instability was proposed more than six decades ago as a mechanism leading to spatial patterning, but it has yet to be exploited in a synthetic biology setting. Here we characterize the Turing instability in a specific gene circuit that can be implemented in vitro or in populations of clonal cells producing short-range activator N-Acyl homoserine lactone (AHL) and long-range inhibitor hydrogen peroxide (H2O2) gas. Slowing the production rate of the AHL-degrading enzyme, AiiA, generates stable fixed states, limit cycle oscillations and Turing patterns. Further tuning of signaling parameters determines local robustness and controls the range of unstable wavenumbers in the patterning regime. These findings provide a roadmap for optimizing spatial patterns of gene expression based on familiar quorum and gas sensitive E. coli promoters. The circuit design and predictions may be useful for (re)programming spatial dynamics in synthetic and natural gene expression systems.

Influence of oscillatory centrifugal forces on the mechanism of Turing pattern formation

Constantly acting centrifugal forces on Turing pattern forming systems have been observed to induce orientation and wavelength changes on Turing structures. Here, we will consider a periodic modulation of such centrifugal forces and their effects on pattern formation. Depending on the oscillation period the system exhibits a wide variety of stationary (stripes, H(0), etc.) or nonstationary patterns (black eyes, etc.), as well as transitions and instabilities such as Eckhaus, zigzag, etc. In this paper, a detailed description of the different patterns and patterning mechanisms will be described and understood within the previous context. The system considered is the Belousov-Zhabotinsky reaction encapsulated in AOT micelles modeled by the adapted version of the Oregonator model.

Endogenous voltage gradients as mediators of cell-cell communication: strategies for investigating bioelectrical signals during pattern formation

Alongside the well-known chemical modes of cell-cell communication, we find an important and powerful system of bioelectrical signaling: changes in the resting voltage potential (Vmem) of the plasma membrane driven by ion channels, pumps and gap junctions. Slow Vmem changes in all cells serve as a highly conserved, information-bearing pathway that regulates cell proliferation, migration and differentiation. In embryonic and regenerative pattern formation and in the disorganization of neoplasia, bioelectrical cues serve as mediators of large-scale anatomical polarity, organ identity and positional information. Recent developments have resulted in tools that enable a high-resolution analysis of these biophysical signals and their linkage with upstream and downstream canonical genetic pathways. Here, we provide an overview for the study of bioelectric signaling, focusing on state-of-the-art approaches that use molecular physiology and developmental genetics to probe the roles of bioelectric events functionally. We highlight the logic, strategies and well-developed technologies that any group of researchers can employ to identify and dissect ionic signaling components in their own work and thus to help crack the bioelectric code. The dissection of bioelectric events as instructive signals enabling the orchestration of cell behaviors into large-scale coherent patterning programs will enrich on-going work in diverse areas of biology, as biophysical factors become incorporated into our systems-level understanding of cell interactions.

Turing patterns and apparent competition in predator-prey food webs on networks

Reaction-diffusion systems may lead to the formation of steady-state heterogeneous spatial patterns, known as Turing patterns. Their mathematical formulation is important for the study of pattern formation in general and plays central roles in many fields of biology, such as ecology and morphogenesis. Here we show that Turing patterns may have a decisive role in shaping the abundance distribution of predators and prey living in patchy landscapes. We extend the original model proposed by Nakao and Mikhailov [Nat. Phys. 6, 544 (2010)] by considering food chains with several interacting pairs of prey and predators distributed on a scale-free network of patches. We identify patterns of species distribution displaying high degrees of apparent competition driven by Turing instabilities. Our results provide further indication that differences in abundance distribution among patches can be generated dynamically by self organized Turing patterns and not only by intrinsic environmental heterogeneity.

Magnetic control of Dictyostelium aggregation

We report the control of cell migration by external magnetic forces during the early stage of Dictysostelium discoideum morphogenesis. Magnetically labeled aggregating cells respond to the presence of a magnetic field created by a thin magnetic tip: forces as low as 30 pN are sufficient to elicit the aggregation of the cells at the extremity of the tip. This induced magnetotaxis is competitive to classical chemotaxis. We therefore underline the interplay between external mechanical forces and morphogenesis. This magnetic assay will open new possibilities in the study of morphogenesis in Dictyostelium.

Spatial Turing-type Pattern Formation in a Model of Signal Transduction Involving Membrane-based Receptors Coupled by G Proteins

In this paper, a model of signaling pathways involving G proteins is investigated. The model incorporates reaction-diffusion mechanisms in which various reactants participate inside and on the extra-cellular surface membrane. The messenger molecules may diffuse over the surface of the cell membrane and signal transduction across the cell membrane is mediated by membrane receptor bound proteins which connect the genetically controlled biochemical intra-cellular reactions to the production of the second messenger, leading to desired functional responses. Dynamic and steady-state properties of the model are then investigated through weakly nonlinear stability analysis. Turing-type patterns are shown to form robustly under different delineating conditions on the system parameters. The theoretical predictions are then discussed in the context of some recently reported experimental evidence.

The role of trans-membrane signal transduction in turing-type cellular pattern formation

The Turing mechanism (Phil. Trans. R. Soc. B 237 (1952) 37) for the production of a broken spatial symmetry in an initially homogeneous system of reacting and diffusing substances has attracted much interest as a potential model for certain aspects of morphogenesis (Models of Biological Pattern Formation, Academic Press, London, 1982; Nature 376 (1995) 765) such as pre-patterning in the embryo. The two features necessary for the formation of Turing patterns are short-range autocatalysis and long-range inhibition (Kybernetik 12 (1972) 30) which usually only occur when the diffusion rate of the inhibitor is significantly greater than that of the activator. This observation has sometimes been used to cast doubt on applicability of the Turing mechanism to cellular patterning since many messenger molecules that diffuse between cells do so at more-or-less similar rates. Here we show that Turing-type patterns will be able to robustly form under a wide variety of realistic physiological conditions though plausible mechanisms of intra-cellular chemical communication without relying on differences in diffusion rates. In the mechanism we propose, reactions occur within cells. Signal transduction leads to the production of messenger molecules, which diffuse between cells at approximately equal rates, coupling the reactions occurring in different cells. These mechanisms also suggest how this process can be controlled in a rather precise way by the genetic machinery of the cell.

Rapid patterning and zonal differentiation in a two-dimensionalDictyosteliumcell mass: the role of pH and ammonia

Recently it was demonstrated that a rapidly forming, self-organizing pattern that emerges within two-dimensional Dictyostelium discoideumcell cultures could later give rise to stripes of distinct zones, each comprising different cell types. Here we report physiological aspects of the initial rapid patterning and its relationship to cell differentiation. We found that as the temperature is lowered the characteristic length of the pattern increases. From this we estimated the activation energy of the patterning kinetics. Fluorescence of fluorescein-conjugated dextran revealed that the cytosolic pH of cells in the inside zone becomes lower than that in the outer zone facing the air. The patterning could be inhibited by addition of the plasma-membrane proton pump inhibitors diethystilbestrol (DES) or miconazole. Preincubation of cells with weak acid delayed the timing of the patterning, whereas weak base hastened it. A pH-indicating dye revealed localized accumulation of ammonia in the extracellular space. These results suggest that gradients of secreted metabolites may be directly responsible for the rapid patterning and its consequence on cell differentiation in a confined geometrical situation. Possible diffusible candidate molecules and a reaction scheme coupled to the imposed oxygen gradient are discussed.

Spatial patterns in ant colonies

The origins of large-scale spatial patterns in biology have been an important source of theoretical speculation since the pioneering work by Turing (1952) on the chemical basis of morphogenesis. Knowing how these patterns emerge and their functional role is important to our understanding of the evolution of biocomplexity and the role played by self organization. However, so far, conclusive evidence for local activation-long-range inhibition mechanisms in real biological systems has been elusive. Here a well-defined experimental and theoretical analysis of the pattern formation dynamics exhibited by clustering behavior in ant colonies is presented. These experiments and a simple mathematical model show that these colonies do indeed use this type of mechanism. All microscopic variables have been measured and provide the first evidence, to our knowledge, for this type of self-organized behavior in complex biological systems, supporting early conjectures about its role in the organization of insect societies.

Slow time evolution of two-time-scale reaction-diffusion systems: the physical origin of nondiffusive transport

We study, from a mesoscopic point of view, the slow time-scale dynamics of a mixture of chemicals in which there is a chemical reaction that occurs much faster than all other processes, including diffusion. For a simple paradigmatic model reaction, it is possible to find a reduced set of dynamical equations analytically. This procedure, which yields the same mean field equations as the macroscopic approach described by Strier and Dawson [J. Chem. Phys, 112, 825 (2000)], clarifies the physical origin of some of the terms that appear in the reduced reaction-diffusion equations, such as "negative density dependent cross diffusion terms," whose actual meaning is hard to assess within the macroscopic framework. We also present a two-time-scale reactive lattice gas automaton with which it is possible to check the validity of the analytical results and the conditions under which the reduced description holds. Using this lattice gas we also show how the differential interaction with immobile species can give rise to the formation of stable Turing patterns in a system where all the other chemicals diffuse approximately at the same rate.

Not being the wrong size

Size regulation is a never-ending problem. Many of us worry that parts of ourselves are too big whereas other parts are too small. How organisms--and their tissues--are programmed to be a specific size, how this size is maintained, and what might cause something to become the wrong size, are key problems in developmental biology. But what are the mechanisms that regulate the size of multicellular structures?

Rapid patterning in 2-D cultures of Dictyostelium cells and its relationship to zonal differentiation

Rapid patterning has been observed in confined 2-D cultures of Dictyostelium discoideum Ax-2 cells as an outer dark zone and a inner light zone. The width of outer zone was usually approximately100 microm, irrespective of the size of cell masses under atmospheric conditions. The width of the outer zone, however, changed depending on external O2 concentrations and reached up to 250 microm at 100% O2. A clear regional difference in tetramethyl rhodamine methyl ester (TMRM) staining was noticed between the outer zone and the inner zone: the inner zone was more strongly stained with TMRM than the outer zone, which faced the air. Using inhibitors of oxidative phosphorylation (dinitrophenol (DNP) or NaN3) and a specific inhibitor of CN-resistant respiration (benzohydroxamic acid (BHAM)), it has been demonstrated that the outer zone is basically formed by the O2 threshold for oxidative phosphorylation, while the inner cells mainly perform cyanide-resistant respiration. When cells around the early mound stage (just before prestalk and prespore differentiation) were cultured as 2-D cell masses, ecmA-expressing cells (pstA cells), ecmB-expressing cells (pstB cells) and D19-expressing cells (prespore; psp cells), arose in a position-dependent manner in the outer zone. In the inner zone, cell motility seemed to be markedly impaired and neither prestalk nor prespore differentiation occurred. In addition, once-differentiated prespore cells were found to dedifferentiate rapidly in the inner zone. The reason for dedifferentiation as well as for failure of cells to differentiate in the inner zone is discussed with reference to O2 radicals.