Pattern formation mechanisms of self-organizing reaction-diffusion systems

A 3D micro-printed single cell micro-niche with asymmetric niche signals - An in vitro model for asymmetric cell division study

Intricate microenvironment signals orchestrate to affect cell behavior and fate during tissue morphogenesis. However, the underlying mechanisms on how specific local niche signals influence cell behavior and fate are not fully understood, owing to the lack of in vitro platform able to precisely, quantitatively, spatially, and independently manipulate individual niche signals. Here, microarrays of protein-based 3D single cell micro-niche (3D-SCμN), with precisely engineered biophysical and biochemical niche signals, are micro-printed by a multiphoton microfabrication and micropatterning technology. Mouse embryonic stem cell (mESC) is used as the model cell to study how local niche signals affect stem cell behavior and fate. By precisely engineering the internal microstructures of the 3D SCμNs, we demonstrate that the cell division direction can be controlled by the biophysical niche signals, in a cell shape-independent manner. After confining the cell division direction to a dominating axis, single mESCs are exposed to asymmetric biochemical niche signals, specifically, cell-cell adhesion molecule on one side and extracellular matrix on the other side. We demonstrate that, symmetry-breaking (asymmetric) niche signals successfully trigger cell polarity formation and bias the orientation of asymmetric cell division, the mitosis process resulting in two daughter cells with differential fates, in mESCs.

Computational methods for biofabrication in tissue engineering and regenerative medicine - a literature review

This literature review rigorously examines the growing scientific interest in computational methods for Tissue Engineering and Regenerative Medicine biofabrication, a leading-edge area in biomedical innovation, emphasizing the need for accurate, multi-stage, and multi-component biofabrication process models. The paper presents a comprehensive bibliometric and contextual analysis, followed by a literature review, to shed light on the vast potential of computational methods in this domain. It reveals that most existing methods focus on single biofabrication process stages and components, and there is a significant gap in approaches that utilize accurate models encompassing both biological and technological aspects. This analysis underscores the indispensable role of these methods in understanding and effectively manipulating complex biological systems and the necessity for developing computational methods that span multiple stages and components. The review concludes that such comprehensive computational methods are essential for developing innovative and efficient Tissue Engineering and Regenerative Medicine biofabrication solutions, driving forward advancements in this dynamic and evolving field.

Arp2/3-dependent endocytosis ensures Cdc42 oscillations by removing Pak1-mediated negative feedback

The GTPase Cdc42 regulates polarized growth in most eukaryotes. In the bipolar yeast Schizosaccharomyces pombe, Cdc42 activation cycles periodically at sites of polarized growth. These periodic cycles are caused by alternating positive feedback and time-delayed negative feedback loops. At each polarized end, negative feedback is established when active Cdc42 recruits the Pak1 kinase to prevent further Cdc42 activation. It is unclear how Cdc42 activation returns to each end after Pak1-dependent negative feedback. We find that disrupting branched actin-mediated endocytosis disables Cdc42 reactivation at the cell ends. Using experimental and mathematical approaches, we show that endocytosis-dependent Pak1 removal from the cell ends allows the Cdc42 activator Scd1 to return to that end to enable reactivation of Cdc42. Moreover, we show that Pak1 elicits its own removal via activation of endocytosis. These findings provide a deeper insight into the self-organization of Cdc42 regulation and reveal previously unknown feedback with endocytosis in the establishment of cell polarity.

Hydrocortisone treatment as a tool to study conjunctival placode induction

BACKGROUND

Conjunctival placodes are a series of placodes that develop into the conjunctival (scleral) papillae and ultimately induce a series of scleral ossicles in the eyes of many vertebrates. This study establishes a hydrocortisone injection procedure (incl. dosage) that consistently inhibits all conjunctival papillae in the embryonic chicken eye. The effects of this hydrocortisone treatment on apoptosis, vasculature, and placode-related gene expression were assessed.

RESULTS

Hydrocortisone treatment does not increase apoptotic cell death or have a major effect on the ciliary artery or vascular plexus in the eye. β-catenin and Eda expression levels were not significantly altered following hydrocortisone treatment, despite the absence of conjunctival papillae. Notably, Fgf20 expression was significantly reduced following hydrocortisone treatment, and the distribution of β-catenin was altered.

CONCLUSIONS

Our study showed that conjunctival papillae induction begins as early as HH27.5 (E5.5). Hydrocortisone treatment reduces Fgf20 expression independently of β-catenin and Eda and may instead affect other members of the Wnt/β-catenin or Eda/Edar pathways, or it may affect the ability of morphogens to diffuse through the extracellular matrix. This study contributes to a growing profile of gene expression data during placode development and enhances our understanding of how some vertebrate eyes develop these fascinating bones.

Contrasting philosophical and scientific views in the long history of studying the generation of form in development

Focusing on the opposing ways of thinking of philosophers and scientists to explain the generation of form in biological development, I show that today's controversies over explanations of early development bear fundamental similarities to the dichotomy of preformation theory versus epigenesis in Greek antiquity. They are related to the acceptance or rejection of the idea of a physical form of what today would be called information for the generating of the embryo as a necessary pre-requisite for specific development and heredity. As a recent example, I scrutinize the dichotomy of genomic causality versus self-organization in 20th and 21st century theories of the generation of form. On the one hand, the generation of patterns and form, as well as the constant outcome in development, are proposed to be causally related to something that is "preformed" in the germ cells, the nucleus of germ cells, or the genome. On the other hand, it is proposed that there is no pre-existing form or information, and development is seen as a process where genuinely new characters emerge from formless matter, either by immaterial "forces of life," or by physical-chemical processes of self-organization. I also argue that these different ways of thinking and the research practices associated with them are not equivalent, and maintain that it is impossible to explain the generation of form and constant outcome of development without the assumption of the transmission of pre-existing information in the form of DNA sequences in the genome. Only in this framework of "preformed" information can "epigenesis" in the form of physical and chemical processes of self-organization play an important role.

Mechanical state transitions in the regulation of tissue form and function

From embryonic development, postnatal growth and adult homeostasis to reparative and disease states, cells and tissues undergo constant changes in genome activity, cell fate, proliferation, movement, metabolism and growth. Importantly, these biological state transitions are coupled to changes in the mechanical and material properties of cells and tissues, termed mechanical state transitions. These mechanical states share features with physical states of matter, liquids and solids. Tissues can switch between mechanical states by changing behavioural dynamics or connectivity between cells. Conversely, these changes in tissue mechanical properties are known to control cell and tissue function, most importantly the ability of cells to move or tissues to deform. Thus, tissue mechanical state transitions are implicated in transmitting information across biological length and time scales, especially during processes of early development, wound healing and diseases such as cancer. This Review will focus on the biological basis of tissue-scale mechanical state transitions, how they emerge from molecular and cellular interactions, and their roles in organismal development, homeostasis, regeneration and disease.

Perturbation of periodic spot-generation balance leads to diversified pigmentation patterning of harlequin Phalaenopsis orchids: in silico prediction

BACKGROUND

A retrotransposon HORT1 in the promoter of the anthocyanin activator gene PeMYB11, microRNA858 (miR858) that targets PeMYB11, and a repressor PeMYBx have been implicated in pigmentation patterning diversity of harlequin Phalaenopsis orchids. However, the interrelationship among them remains to be elucidated.

RESULTS

To understand how these factors interact to generate anthocyanin spots in Phalaenopsis, we successfully developed a mathematical model based on the known reaction-diffusion system to simulate their interplay and refined the conceptual biological model. Intriguingly, the expression of both PeMYBx and PeMYB11 were in phase for purple spot formation, even though they showed adverse effects on anthocyanin accumulations. An increase in the self-activation rate of PeMYB11 resulted in the increased size of purple spots, but no effects on spot fusion. Decreased degradation rate of miR858 in the purple regions, led to disruption of the formation of spotted pigmentation patterning and a full-red pigmentation pattern. Significantly, the reduced miR858 level promotes the fusion of large dark purple dots induced by the solo-LTR of HORT1, eventually generating the purple patches. In addition, the spatially heterogeneous insertion of HORT1 caused by the remnant solo-LTR of HORT1 derived from random homologous unequal recombination of HORT1 in individual cells of floral organs could explain the diverse pigmentation patterning of harlequin Phalaenopsis.

CONCLUSIONS

This devised model explains how HORT1 and miR858 regulate the formation of the pigmentation patterning and holds great promise for developing efficient and innovative approaches to breeding harlequin Phalaenopsis orchids.

Instabilities and self-organization in spatiotemporal epidemic dynamics driven by nonlinearity and noise

Theoretical analysis of epidemic dynamics has attracted significant attention in the aftermath of the COVID-19 pandemic. In this article, we study dynamic instabilities in a spatiotemporal compartmental epidemic model represented by a stochastic system of coupled partial differential equations (SPDE). Saturation effects in infection spread-anchored in physical considerations-lead to strong nonlinearities in the SPDE. Our goal is to study the onset of dynamic, Turing-type instabilities, and the concomitant emergence of steady-state patterns under the interplay between three critical model parameters-the saturation parameter, the noise intensity, and the transmission rate. Employing a second-order perturbation analysis to investigate stability, we uncover both diffusion-driven and noise-induced instabilities and corresponding self-organized distinct patterns of infection spread in the steady state. We also analyze the effects of the saturation parameter and the transmission rate on the instabilities and the pattern formation. In summary, our results indicate that the nuanced interplay between the three parameters considered has a profound effect on the emergence of dynamical instabilities and therefore on pattern formation in the steady state. Moreover, due to the central role played by the Turing phenomenon in pattern formation in a variety of biological dynamic systems, the results are expected to have broader significance beyond epidemic dynamics.

Stem Cells and Differentiation in Vascular Tissues

Plant vascular tissues are crucial for the long-distance transport of water, nutrients, and a multitude of signal molecules throughout the plant body and, therefore, central to plant growth and development. The intricate development of vascular tissues is orchestrated by unique populations of dedicated stem cells integrating endogenous as well as environmental cues. This review summarizes our current understanding of vascular-related stem cell biology and of vascular tissue differentiation. We present an overview of the molecular and cellular mechanisms governing the maintenance and fate determination of vascular stem cells and highlight the interplay between intrinsic and external cues. In this context, we emphasize the role of transcription factors, hormonal signaling, and epigenetic modifications. We also discuss emerging technologies and the large repertoire of cell types associated with vascular tissues, which have the potential to provide unprecedented insights into cellular specialization and anatomical adaptations to distinct ecological niches.

In situ enzymatic control of colloidal phoresis and catalysis through hydrolysis of ATP

The ability to sense chemical gradients and respond with directional motility and chemical activity is a defining feature of complex living systems. There is a strong interest among scientists to design synthetic systems that emulate these properties. Here, we realize and control such behaviors in a synthetic system by tailoring multivalent interactions of adenosine nucleotides with catalytic microbeads. We first show that multivalent interactions of the bead with gradients of adenosine mono-, di- and trinucleotides (AM/D/TP) control both the phoretic motion and a proton-transfer catalytic reaction, and find that both effects are diminished greatly with increasing valence of phosphates. We exploit this behavior by using enzymatic hydrolysis of ATP to AMP, which downregulates multivalent interactivity in situ. This produces a sudden increase in transport of the catalytic microbeads (a phoretic jump), which is accompanied by increased catalytic activity. Finally, we show how this enzymatic activity can be systematically tuned, leading to simultaneous in situ spatial and temporal control of the location of the microbeads, as well as the products of the reaction that they catalyze. These findings open up new avenues for utilizing multivalent interaction-mediated programming of complex chemo-mechanical behaviors into active systems.

Patterning of the cell cortex by Rho GTPases

The Rho GTPases - RHOA, RAC1 and CDC42 - are small GTP binding proteins that regulate basic biological processes such as cell locomotion, cell division and morphogenesis by promoting cytoskeleton-based changes in the cell cortex. This regulation results from active (GTP-bound) Rho GTPases stimulating target proteins that, in turn, promote actin assembly and myosin 2-based contraction to organize the cortex. This basic regulatory scheme, well supported by in vitro studies, led to the natural assumption that Rho GTPases function in vivo in an essentially linear matter, with a given process being initiated by GTPase activation and terminated by GTPase inactivation. However, a growing body of evidence based on live cell imaging, modelling and experimental manipulation indicates that Rho GTPase activation and inactivation are often tightly coupled in space and time via signalling circuits and networks based on positive and negative feedback. In this Review, we present and discuss this evidence, and we address one of the fundamental consequences of coupled activation and inactivation: the ability of the Rho GTPases to self-organize, that is, direct their own transition from states of low order to states of high order. We discuss how Rho GTPase self-organization results in the formation of diverse spatiotemporal cortical patterns such as static clusters, oscillatory pulses, travelling wave trains and ring-like waves. Finally, we discuss the advantages of Rho GTPase self-organization and pattern formation for cell function.

Enteric Nervous System Striped Patterning and Disease: Unexplored Pathophysiology

The enteric nervous system (ENS) controls gastrointestinal (GI) motility, and defects in ENS development underlie pediatric GI motility disorders. In disorders such as Hirschsprung's disease (HSCR), pediatric intestinal pseudo-obstruction (PIPO), and intestinal neuronal dysplasia type B (INDB), ENS structure is altered with noted decreased neuronal density in HSCR and reports of increased neuronal density in PIPO and INDB. The developmental origin of these structural deficits is not fully understood. Here, we review the current understanding of ENS development and pediatric GI motility disorders incorporating new data on ENS structure. In particular, emerging evidence demonstrates that enteric neurons are patterned into circumferential stripes along the longitudinal axis of the intestine during mouse and human development. This novel understanding of ENS structure proposes new questions about the pathophysiology of pediatric GI motility disorders. If the ENS is organized into stripes, could the observed changes in enteric neuron density in HSCR, PIPO, and INDB represent differences in the distribution of enteric neuronal stripes? We review mechanisms of striped patterning from other biological systems and propose how defects in striped ENS patterning could explain structural deficits observed in pediatric GI motility disorders.

A diffusible small-RNA-based Turing system dynamically coordinates organ polarity

The formation of a flat and thin leaf presents a developmentally challenging problem, requiring intricate regulation of adaxial-abaxial (top-bottom) polarity. The patterning principles controlling the spatial arrangement of these domains during organ growth have remained unclear. Here we show that this regulation in Arabidopsis thaliana is achieved by an organ-autonomous Turing reaction-diffusion system centred on mobile small RNAs. The data illustrate how Turing dynamics transiently instructed by prepatterned information is sufficient to self-sustain properly oriented polarity in a dynamic, growing organ, presenting intriguing parallels to left-right patterning in the vertebrate embryo. Computational modelling demonstrates that this self-organizing system continuously adapts to coordinate the robust planar polarity of a flat leaf while affording flexibility to generate the tissue patterns of evolutionarily diverse organ shapes. Our findings identify a small-RNA-based Turing network as a dynamic regulator of organ polarity that accounts for leaf shape diversity at the level of the individual organ, plant or species.

Turing Instabilities are Not Enough to Ensure Pattern Formation

Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction-diffusion theory, which connects cellular signalling and transport with the development of growth and form. Extensive literature focuses on the linear stability analysis of homogeneous equilibria in these systems, culminating in a set of conditions for transport-driven instabilities that are commonly presumed to initiate self-organisation. We demonstrate that a selection of simple, canonical transport models with only mild multistable non-linearities can satisfy the Turing instability conditions while also robustly exhibiting only transient patterns. Hence, a Turing-like instability is insufficient for the existence of a patterned state. While it is known that linear theory can fail to predict the formation of patterns, we demonstrate that such failures can appear robustly in systems with multiple stable homogeneous equilibria. Given that biological systems such as gene regulatory networks and spatially distributed ecosystems often exhibit a high degree of multistability and nonlinearity, this raises important questions of how to analyse prospective mechanisms for self-organisation.

Turing Pattern Formation in Reaction-Cross-Diffusion Systems with a Bilayer Geometry

Conditions for self-organisation via Turing's mechanism in biological systems represented by reaction-diffusion or reaction-cross-diffusion models have been extensively studied. Nonetheless, the impact of tissue stratification in such systems is under-explored, despite its ubiquity in the context of a thin epithelium overlying connective tissue, for instance the epidermis and underlying dermal mesenchyme of embryonic skin. In particular, each layer can be subject to extensively different biochemical reactions and transport processes, with chemotaxis - a special case of cross-diffusion - often present in the mesenchyme, contrasting the solely molecular transport typically found in the epidermal layer. We study Turing patterning conditions for a class of reaction-cross-diffusion systems in bilayered regions, with a thin upper layer and coupled by a linear transport law. In particular, the role of differential transport through the interface is explored together with the presence of asymmetry between the homogeneous equilibria of the two layers. A linear stability analysis is carried out around a spatially homogeneous equilibrium state in the asymptotic limit of weak and strong coupling strengths, where quantitative approximations of the bifurcation curve can be computed. Our theoretical findings, for an arbitrary number of reacting species, reveal quantitative Turing conditions, highlighting when the coupling mechanism between the layered regions can either trigger patterning or stabilize a spatially homogeneous equilibrium regardless of the independent patterning state of each layer. We support our theoretical results through direct numerical simulations, and provide an open source code to explore such systems further.

PatU3 plays a central role in coordinating cell division and differentiation in pattern formation of filamentous cyanobacterium Nostoc sp. PCC 7120

Spatial periodic signal for cell differentiation in some multicellular organisms is generated according to Turing's principle for pattern formation. How a dividing cell responds to the signal of differentiation is addressed with the filamentous cyanobacterium Nostoc sp. PCC 7120, which forms the patterned distribution of heterocysts. We show that differentiation of a dividing cell was delayed until its division was completed and only one daughter cell became heterocyst. A mutant of patU3, which encodes an inhibitor of heterocyst formation, showed no such delay and formed heterocyst pairs from the daughter cells of cell division or dumbbell-shaped heterocysts from the cells undergoing cytokinesis. The patA mutant, which forms heterocysts only at the filament ends, restored intercalary heterocysts by a single nucleotide mutation of patU3, and double mutants of patU3/patA and patU3/hetF had the phenotypes of the patU3 mutant. We provide evidence that HetF, which can degrade PatU3, is recruited to cell divisome through its C-terminal domain. A HetF mutant with its N-terminal peptidase domain but lacking the C-terminal domain could not prevent the formation of heterocyst pairs, suggesting that the divisome recruitment of HetF is needed to sequester HetF for the delay of differentiation in dividing cells. Our study demonstrates that PatU3 plays a key role in cell-division coupled control of differentiation.

Novel Aspects in Pattern Formation Arise from Coupling Turing Reaction-Diffusion and Chemotaxis

Recent experimental studies on primary hair follicle formation and feather bud morphogenesis indicate a coupling between Turing-type diffusion driven instability and chemotactic patterning. Inspired by these findings we develop and analyse a mathematical model that couples chemotaxis to a reaction-diffusion system exhibiting diffusion-driven (Turing) instability. While both systems, reaction-diffusion systems and chemotaxis, can independently generate spatial patterns, we were interested in how the coupling impacts the stability of the system, parameter region for patterning, pattern geometry, as well as the dynamics of pattern formation. We conduct a classical linear stability analysis for different model structures, and confirm our results by numerical analysis of the system. Our results show that the coupling generally increases the robustness of the patterning process by enlarging the pattern region in the parameter space. Concerning time scale and pattern regularity, we find that an increase in the chemosensitivity can speed up the patterning process for parameters inside and outside of the Turing space, but generally reduces spatial regularity of the pattern. Interestingly, our analysis indicates that pattern formation can also occur when neither the Turing nor the chemotaxis system can independently generate pattern. On the other hand, for some parameter settings, the coupling of the two processes can extinguish the pattern formation, rather than reinforce it. These theoretical findings can be used to corroborate the biological findings on morphogenesis and guide future experimental studies. From a mathematical point of view, this work sheds a light on coupling classical pattern formation systems from the parameter space perspective.

Dynamic supramolecular hydrogels mediated by chemical reactions

Supramolecular self-assembly in a biological system is usually dominated by sophisticated metabolic processes (chemical reactions) such as catalysis of enzymes and consumption of high energy chemicals, leading to groups of biomolecules with unique dynamics and functions in an aqueous environment. In recent years, increasing efforts have been made to couple chemical reactions to molecular self-assembly, with the aim of creating supramolecular materials with lifelike properties and functions. In this feature article, after summarising the work of chemical reaction mediated supramolecular hydrogels, we first focus on a typical example where dynamic self-assembly of molecular hydrogels is activated by in situ formation of a hydrazone bond in water. We discuss how the formation of the hydrazone-based supramolecular hydrogels can be controlled in time and space. After that, we describe transient assembly of supramolecular hydrogels powered by out-of-equilibrium chemical reaction networks regulated by chemical fuels, which show unique properties such as finite lifetime, dynamic structures, and regenerative capabilities. Finally, we provide a perspective on the future investigations that need to be done urgently, which range from fundamental research to real-life applications of dynamic supramolecular hydrogels.

The Arp2/3 complex promotes periodic removal of Pak1-mediated negative feedback to facilitate anticorrelated Cdc42 oscillations

The conserved GTPase Cdc42 is a major regulator of polarized growth in most eukaryotes. Cdc42 periodically cycles between active and inactive states at sites of polarized growth. These periodic cycles are caused by positive feedback and time-delayed negative feedback loops. In the bipolar yeast S. pombe, both growing ends must regulate Cdc42 activity. At each cell end, Cdc42 activity recruits the Pak1 kinase which prevents further Cdc42 activation thus establishing negative feedback. It is unclear how Cdc42 activation returns to the end after Pak1-dependent negative feedback. Using genetic and chemical perturbations, we find that disrupting branched actin-mediated endocytosis disables Cdc42 reactivation at the cell ends. With our experimental data and mathematical models, we show that endocytosis-dependent Pak1 removal from the cell ends allows the Cdc42 activator Scd1 to return to that end to enable reactivation of Cdc42. Moreover, we show that Pak1 elicits its own removal via activation of endocytosis. In agreement with these observations, our model and experimental data show that in each oscillatory cycle, Cdc42 activation increases followed by an increase in Pak1 recruitment at that end. These findings provide a deeper insight into the self-organization of Cdc42 regulation and reveal previously unknown feedback with endocytosis in the establishment of cell polarity.

Dynamic Growth of Macroscopically Structured Supramolecular Hydrogels through Orchestrated Reaction-Diffusion

Living organisms are capable of dynamically changing their structures for adaptive functions through sophisticated reaction-diffusion processes. Here we show how active supramolecular hydrogels with programmable lifetimes and macroscopic structures can be created by relying on a simple reaction-diffusion strategy. Two hydrogel precursors (poly(acrylic acid) PAA/CaCl2 and Na2 CO3 ) diffuse from different locations and generate amorphous calcium carbonate (ACC) nanoparticles at the diffusional fronts, leading to the formation of hydrogel structures driven by electrostatic interactions between PAA and ACC nanoparticles. Interestingly, the formed hydrogels are capable of autonomously disintegrating over time because of a delayed influx of electrostatic-interaction inhibitors (NaCl). The hydrogel growth process is well explained by a reaction-diffusion model which offers a theoretical means to program the dynamic growth of structured hydrogels. Furthermore, we demonstrate a conceptual access to dynamic information storage in soft materials using the developed reaction-diffusion strategy. This work may serve as a starting point for the development of life-like materials with adaptive structures and functionalities.

Imaging local diffusion in microstructures using NV-based pulsed field gradient NMR

Understanding diffusion in microstructures plays a crucial role in many scientific fields, including neuroscience, medicine, or energy research. While magnetic resonance (MR) methods are the gold standard for diffusion measurements, spatial encoding in MR imaging has limitations. Here, we introduce nitrogen-vacancy (NV) center-based nuclear MR (NMR) spectroscopy as a powerful tool to probe diffusion within microscopic sample volumes. We have developed an experimental scheme that combines pulsed gradient spin echo (PGSE) with optically detected NV-NMR spectroscopy, allowing local quantification of molecular diffusion and flow. We demonstrate correlated optical imaging with spatially resolved PGSE NV-NMR experiments probing anisotropic water diffusion within an individual model microstructure. Our optically detected PGSE NV-NMR technique opens up prospects for extending the current capabilities of investigating diffusion processes with the future potential of probing single cells, tissue microstructures, or ion mobility in thin film materials for battery applications.

Closing the loop on morphogenesis: a mathematical model of morphogenesis by closed-loop reaction-diffusion

Morphogenesis, the establishment and repair of emergent complex anatomy by groups of cells, is a fascinating and biomedically-relevant problem. One of its most fascinating aspects is that a developing embryo can reliably recover from disturbances, such as splitting into twins. While this reliability implies some type of goal-seeking error minimization over a morphogenic field, there are many gaps with respect to detailed, constructive models of such a process. A common way to achieve reliability is negative feedback, which requires characterizing the existing body shape to create an error signal-but measuring properties of a shape may not be simple. We show how cells communicating in a wave-like pattern could analyze properties of the current body shape. We then describe a closed-loop negative-feedback system for creating reaction-diffusion (RD) patterns with high reliability. Specifically, we use a wave to count the number of peaks in a RD pattern, letting us use a negative-feedback controller to create a pattern with N repetitions, where N can be altered over a wide range. Furthermore, the individual repetitions of the RD pattern can be easily stretched or shrunk under genetic control to create, e.g., some morphological features larger than others. This work contributes to the exciting effort of understanding design principles of morphological computation, which can be used to understand evolved developmental mechanisms, manipulate them in regenerative-medicine settings, or engineer novel synthetic morphology constructs with desired robust behavior.

Collective behavior and self-organization in neural rosette morphogenesis

Neural rosettes develop from the self-organization of differentiating human pluripotent stem cells. This process mimics the emergence of the embryonic central nervous system primordium, i.e., the neural tube, whose formation is under close investigation as errors during such process result in severe diseases like spina bifida and anencephaly. While neural tube formation is recognized as an example of self-organization, we still do not understand the fundamental mechanisms guiding the process. Here, we discuss the different theoretical frameworks that have been proposed to explain self-organization in morphogenesis. We show that an explanation based exclusively on stem cell differentiation cannot describe the emergence of spatial organization, and an explanation based on patterning models cannot explain how different groups of cells can collectively migrate and produce the mechanical transformations required to generate the neural tube. We conclude that neural rosette development is a relevant experimental 2D in-vitro model of morphogenesis because it is a multi-scale self-organization process that involves both cell differentiation and tissue development. Ultimately, to understand rosette formation, we first need to fully understand the complex interplay between growth, migration, cytoarchitecture organization, and cell type evolution.

Steady state of a two-species annihilation process with separated reactants

We describe the steady state of the annihilation process of a one-dimensional system of two initially separated reactants A and B. The parameters that define the dynamical behavior of the system are the diffusion constant, the reaction rate, and the deposition rate. Depending on the ratio between those parameters, the system exhibits a crossover between a diffusion-limited (DL) regime and a reaction-limited (RL) regime. We found that a key quantity to describe the reaction process in the system is the probability p(x_{A},x_{B}) to find the rightmost A (RMA) particle and the leftmost B (LMB) particle at the positions x_{A} and x_{B}, respectively. The statistical behavior of the system in both regimes is described using the density of particles, the gap length distribution x_{B}-x_{A}, the marginal probabilities p_{A}(x_{A}) and p_{B}(x_{B}), and the reaction kernel. For both regimes, this kernel can be approximated by using p(x_{A},x_{B}). We found an excellent agreement between the numerical and analytical results for all calculated quantities despite the reaction process being quite different in both regimes. In the DL regime, the reaction kernel can be approximated by the probability to find the RMA and LMB particles in adjacent sites. In the RL regime, the kernel depends on the marginal probabilities p_{A}(x_{A}) and p_{B}(x_{B}).

Learning system parameters from turing patterns

The Turing mechanism describes the emergence of spatial patterns due to spontaneous symmetry breaking in reaction-diffusion processes and underlies many developmental processes. Identifying Turing mechanisms in biological systems defines a challenging problem. This paper introduces an approach to the prediction of Turing parameter values from observed Turing patterns. The parameter values correspond to a parametrized system of reaction-diffusion equations that generate Turing patterns as steady state. The Gierer-Meinhardt model with four parameters is chosen as a case study. A novel invariant pattern representation based on resistance distance histograms is employed, along with Wasserstein kernels, in order to cope with the highly variable arrangement of local pattern structure that depends on the initial conditions which are assumed to be unknown. This enables us to compute physically plausible distances between patterns, to compute clusters of patterns and, above all, model parameter prediction based on training data that can be generated by numerical model evaluation with random initial data: for small training sets, classical state-of-the-art methods including operator-valued kernels outperform neural networks that are applied to raw pattern data, whereas for large training sets the latter are more accurate. A prominent property of our approach is that only a single pattern is required as input data for model parameter predicion. Excellent predictions are obtained for single parameter values and reasonably accurate results for jointly predicting all four parameter values.

Self-Organization and Genomic Causality in Models of Morphogenesis

The debate about what causes the generation of form and structure in embryological development goes back to antiquity. Most recently, it has focused on the divergent views as to whether the generation of patterns and form in development is a largely self-organized process or is mainly determined by the genome, in particular, complex developmental gene regulatory processes. This paper presents and analyzes pertinent models of pattern formation and form generation in a developing organism in the past and the present, with a special emphasis on Alan Turing's 1952 reaction-diffusion model. I first draw attention to the fact that Turing's paper remained, at first, without a noticeable impact on the community of biologists because purely physical-chemical models were unable to explain embryological development and often also simple repetitive patterns. I then show that from the year 2000 and onwards, Turing's 1952 paper was increasingly cited also by biologists. The model was updated to include gene products and now seemed able to account for the generation of biological patterns, though discrepancies between models and biological reality remained. I then point out Eric Davidson's successful theory of early embryogenesis based on gene-regulatory network analysis and its mathematical modeling that not only was able to provide a mechanistic and causal explanation for gene regulatory events controlling developmental cell fate specification but, unlike reaction-diffusion models, also addressed the effects of evolution and organisms' longstanding developmental and species stability. The paper concludes with an outlook on further developments of the gene regulatory network model.

The emergence of spatial patterns for compartmental reaction kinetics coupled by two bulk diffusing species with comparable diffusivities

Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a central problem in many chemical and biological systems. From a mathematical viewpoint, one key challenge with this theory for two component systems is that stable spatial patterns can typically only occur from a spatially uniform state when a slowly diffusing 'activator' species reacts with a much faster diffusing 'inhibitor' species. However, from a modelling perspective, this large diffusivity ratio requirement for pattern formation is often unrealistic in biological settings since different molecules tend to diffuse with similar rates in extracellular spaces. As a result, one key long-standing question is how to robustly obtain pattern formation in the biologically realistic case where the time scales for diffusion of the interacting species are comparable. For a coupled one-dimensional bulk-compartment theoretical model, we investigate the emergence of spatial patterns for the scenario where two bulk diffusing species with comparable diffusivities are coupled to nonlinear reactions that occur only in localized 'compartments', such as on the boundaries of a one-dimensional domain. The exchange between the bulk medium and the spatially localized compartments is modelled by a Robin boundary condition with certain binding rates. As regulated by these binding rates, we show for various specific nonlinearities that our one-dimensional coupled PDE-ODE model admits symmetry-breaking bifurcations, leading to linearly stable asymmetric steady-state patterns, even when the bulk diffusing species have equal diffusivities. Depending on the form of the nonlinear kinetics, oscillatory instabilities can also be triggered. Moreover, the analysis is extended to treat a periodic chain of compartments. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.

A shark-inspired general model of tooth morphogenesis unveils developmental asymmetries in phenotype transitions

Developmental complexity stemming from the dynamic interplay between genetic and biomechanic factors canalizes the ways genotypes and phenotypes can change in evolution. As a paradigmatic system, we explore how changes in developmental factors generate typical tooth shape transitions. Since tooth development has mainly been researched in mammals, we contribute to a more general understanding by studying the development of tooth diversity in sharks. To this end, we build a general, but realistic, mathematical model of odontogenesis. We show that it reproduces key shark-specific features of tooth development as well as real tooth shape variation in small-spotted catsharks Scyliorhinus canicula. We validate our model by comparison with experiments in vivo. Strikingly, we observe that developmental transitions between tooth shapes tend to be highly degenerate, even for complex phenotypes. We also discover that the sets of developmental parameters involved in tooth shape transitions tend to depend asymmetrically on the direction of that transition. Together, our findings provide a valuable base for furthering our understanding of how developmental changes can lead to both adaptive phenotypic change and trait convergence in complex, phenotypically highly diverse, structures.

Extensive embryonic patterning without cellular differentiation primes the plant epidermis for efficient post-embryonic stomatal activities

Plant leaves feature epidermal stomata that are organized in stereotyped patterns. How does the pattern originate? We provide transcriptomic, imaging, and genetic evidence that Arabidopsis embryos engage known stomatal fate and patterning factors to create regularly spaced stomatal precursor cells. Analysis of embryos from 36 plant species indicates that this trait is widespread among angiosperms. Embryonic stomatal patterning in Arabidopsis is established in three stages: first, broad SPEECHLESS (SPCH) expression; second, coalescence of SPCH and its targets into discrete domains; and third, one round of asymmetric division to create stomatal precursors. Lineage progression is then halted until after germination. We show that the embryonic stomatal pattern enables fast stomatal differentiation and photosynthetic activity upon germination, but it also guides the formation of additional stomata as the leaf expands. In addition, key stomatal regulators are prevented from driving the fate transitions they can induce after germination, identifying stage-specific layers of regulation that control lineage progression during embryogenesis.

Stability of Pattern Formation in Systems with Dynamic Source Regions

We explain the principles of gene expression pattern stabilization in systems of interacting, diffusible morphogens, with dynamically established source regions. Using a reaction-diffusion model with a step-function production term, we identify the phase transition between low-precision indeterminate patterning and the phase in which a traveling, well-defined contact zone between two domains is formed. Our model analytically explains single- and two-gene domain dynamics and provides pattern stability conditions for all possible two-gene regulatory network motifs.

Periodic spatial patterning with a single morphogen

During multicellular development, periodic spatial patterning systems generate repetitive structures, such as digits, vertebrae, and teeth. Turing patterning provides a foundational paradigm for understanding such systems. The simplest Turing systems are believed to require at least two morphogens to generate periodic patterns. Here, using mathematical modeling, we show that a simpler circuit, including only a single diffusible morphogen, is sufficient to generate long-range, spatially periodic patterns that propagate outward from transient initiating perturbations and remain stable after the perturbation is removed. Furthermore, an additional bistable intracellular feedback or operation on a growing cell lattice can make patterning robust to noise. Together, these results show that a single morphogen can be sufficient for robust spatial pattern formation and should provide a foundation for engineering pattern formation in the emerging field of synthetic developmental biology.

The idea of constancy in development and evolution - Scientific and philosophical perspectives

The ability of developmental systems to produce constant phenotypes, even in a wide range of different environments, and the longstanding stability of species are among the most remarkable phenomena in biology. I argue that understanding the longstanding constancy and stability of species or the constant outcome of development in different environments are also prerequisites for explaining stable change (i.e., change that does not consist of random plasticity). Various approaches to account for stable changes in development are based on the causal role of genes and an organized genome, mathematical-physical-chemical models, or a combination of both. I argue that the constancy of developmental outcome and the longstanding stability of species are associated with organisms' structural and organizational hierarchies, particularly highly organized gene-regulatory networks and genetic causality, which are fundamental principles of life. Mathematical-physical-chemical models that marginalize these principles cannot convincingly account for the observed constancy in development and evolution. However, an integration of physical-chemical processes such as reaction-diffusion mechanisms and genome-based mechanisms of form generation has recently proved fruitful in explaining the development of some periodic structures. Constancy and change were also major topoi in ancient Greek philosophy, in which prominent philosophical schools such as the atomists attempted to bridge the antinomy between them by basing stable change on constant entities. I argue that the idea of change, that is, change without losing complexity or even increasing it, being based on modifications of the otherwise reliable transmission of genomes over long periods of time has a historical parallel in the writings of these ancient speculative thinkers, notwithstanding the fundamental differences between the two thought systems.

A group theoretic approach to model comparison with simplicial representations

The complexity of biological systems, and the increasingly large amount of associated experimental data, necessitates that we develop mathematical models to further our understanding of these systems. Because biological systems are generally not well understood, most mathematical models of these systems are based on experimental data, resulting in a seemingly heterogeneous collection of models that ostensibly represent the same system. To understand the system we therefore need to understand how the different models are related to each other, with a view to obtaining a unified mathematical description. This goal is complicated by the fact that a number of distinct mathematical formalisms may be employed to represent the same system, making direct comparison of the models very difficult. A methodology for comparing mathematical models based on their underlying conceptual structure is therefore required. In previous work we developed an appropriate framework for model comparison where we represent models, specifically the conceptual structure of the models, as labelled simplicial complexes and compare them with the two general methodologies of comparison by distance and comparison by equivalence. In this article we continue the development of our model comparison methodology in two directions. First, we present a rigorous and automatable methodology for the core process of comparison by equivalence, namely determining the vertices in a simplicial representation, corresponding to model components, that are conceptually related and the identification of these vertices via simplicial operations. Our methodology is based on considerations of vertex symmetry in the simplicial representation, for which we develop the required mathematical theory of group actions on simplicial complexes. This methodology greatly simplifies and expedites the process of determining model equivalence. Second, we provide an alternative mathematical framework for our model-comparison methodology by representing models as groups, which allows for the direct application of group-theoretic techniques within our model-comparison methodology.

Exploring standards for multicellular mammalian synthetic biology

Synthetic biology is moving towards bioengineering multicellular mammalian systems that are poised to advance tissue engineering, biomedicine, and the food industry. Despite progress, the field lacks a framework of standards that could greatly accelerate further development. Here, we explore the landscape of standards for multicellular mammalian synthetic biology. We discuss the limits of current technical standards and categorise unaddressed parameters into an abstraction hierarchy. We then define the concept of a 'synthetic multicellular mammalian system' and apply our standard hierarchy framework to illustrate how it could aid bioengineering endeavours. We conclude with promising areas that could shape the future of the field, flagging the need for a critical and holistic consideration of standards that requires cross-disciplinary dialogue.

Reaction-diffusion models in weighted and directed connectomes

Connectomes represent comprehensive descriptions of neural connections in a nervous system to better understand and model central brain function and peripheral processing of afferent and efferent neural signals. Connectomes can be considered as a distinctive and necessary structural component alongside glial, vascular, neurochemical, and metabolic networks of the nervous systems of higher organisms that are required for the control of body functions and interaction with the environment. They are carriers of functional epiphenomena such as planning behavior and cognition, which are based on the processing of highly dynamic neural signaling patterns. In this study, we examine more detailed connectomes with edge weighting and orientation properties, in which reciprocal neuronal connections are also considered. Diffusion processes are a further necessary condition for generating dynamic bioelectric patterns in connectomes. Based on our high-precision connectome data, we investigate different diffusion-reaction models to study the propagation of dynamic concentration patterns in control and lesioned connectomes. Therefore, differential equations for modeling diffusion were combined with well-known reaction terms to allow the use of connection weights, connectivity orientation and spatial distances.

Three reaction-diffusion systems Gray-Scott, Gierer-Meinhardt and Mimura-Murray were investigated. For this purpose, implicit solvers were implemented in a numerically stable reaction-diffusion system within the framework of neuroVIISAS. The implemented reaction-diffusion systems were applied to a subconnectome which shapes the mechanosensitive pathway that is strongly affected in the multiple sclerosis demyelination disease. It was found that demyelination modeling by connectivity weight modulation changes the oscillations of the target region, i.e. the primary somatosensory cortex, of the mechanosensitive pathway.

In conclusion, a new application of reaction-diffusion systems to weighted and directed connectomes has been realized. Because the implementation were performed in the neuroVIISAS framework many possibilities for the study of dynamic reaction-diffusion processes in empirical connectomes as well as specific randomized network models are available now.

Spatial programming of self-organizing chemical systems using sustained physicochemical gradients from reaction, diffusion and hydrodynamics

Living organisms employ chemical self-organization to build structures, and inspire new strategies to design synthetic systems that spontaneously take a particular form, via a combination of integrated chemical reactions, assembly pathways and physicochemical processes. However, spatial programmability that is required to direct such self-organization is a challenge to control. Thermodynamic equilibrium typically brings about a homogeneous solution, or equilibrium structures such as supramolecular complexes and crystals. This perspective addresses out-of-equilibrium gradients that can be driven by coupling chemical reaction, diffusion and hydrodynamics, and provide spatial differentiation in the self-organization of molecular, ionic or colloidal building blocks in solution. These physicochemical gradients are required to (1) direct the organization from the starting conditions (e.g. a homogeneous solution), and (2) sustain the organization, to prevent it from decaying towards thermodynamic equilibrium. We highlight four different concepts that can be used as a design principle to establish such self-organization, using chemical reactions as a driving force to sustain the gradient and, ultimately, program the characteristics of the gradient: (1) reaction-diffusion coupling; (2) reaction-convection; (3) the Marangoni effect and (4) diffusiophoresis. Furthermore, we outline their potential as attractive pathways to translate chemical reactions and molecular/colloidal assembly into organization of patterns in solution, (dynamic) self-assembled architectures and collectively moving swarms at the micro-, meso- and macroscale, exemplified by recent demonstrations in the literature.

Nanofiltration Membranes with Crumpled Polyamide Films: A Critical Review on Mechanisms, Performances, and Environmental Applications

Nanofiltration (NF) membranes have been widely applied in many important environmental applications, including water softening, surface/groundwater purification, wastewater treatment, and water reuse. In recent years, a new class of piperazine (PIP)-based NF membranes featuring a crumpled polyamide layer has received considerable attention because of their great potential for achieving dramatic improvements in membrane separation performance. Since the report of novel crumpled Turing structures that exhibited an order of magnitude enhancement in water permeance ( Science 2018, 360 (6388), 518-521), the number of published research papers on this emerging topic has grown exponentially to approximately 200. In this critical review, we provide a systematic framework to classify the crumpled NF morphologies. The fundamental mechanisms and fabrication methods involved in the formation of these crumpled morphologies are summarized. We then discuss the transport of water and solutes in crumpled NF membranes and how these transport phenomena could simultaneously improve membrane water permeance, selectivity, and antifouling performance. The environmental applications of these emerging NF membranes are highlighted, and future research opportunities/needs are identified. The fundamental insights in this review provide critical guidance on the further development of high-performance NF membranes tailored for a wide range of environmental applications.

Boundary Conditions Cause Different Generic Bifurcation Structures in Turing Systems

Turing’s theory of morphogenesis is a generic mechanism to produce spatial patterning from near homogeneity. Although widely studied, we are still able to generate new results by returning to common dogmas. One such widely reported belief is that the Turing bifurcation occurs through a pitchfork bifurcation, which is true under zero-flux boundary conditions. However, under fixed boundary conditions, the Turing bifurcation becomes generically transcritical. We derive these algebraic results through weakly nonlinear analysis and apply them to the Schnakenberg kinetics. We observe that the combination of kinetics and boundary conditions produce their own uncommon boundary complexities that we explore numerically. Overall, this work demonstrates that it is not enough to only consider parameter perturbations in a sensitivity analysis of a specific application. Variations in boundary conditions should also be considered.

Information Hiding Based on Statistical Features of Self-Organizing Patterns

A computational technique for the determination of optimal hiding conditions of a digital image in a self-organizing pattern is presented in this paper. Three statistical features of the developing pattern (the Wada index based on the weighted and truncated Shannon entropy, the mean of the brightness of the pattern, and the p-value of the Kolmogorov-Smirnov criterion for the normality testing of the distribution function) are used for that purpose. The transition from the small-scale chaos of the initial conditions to the large-scale chaos of the developed pattern is observed during the evolution of the self-organizing system. Computational experiments are performed with the stripe-type patterns, spot-type patterns, and unstable patterns. It appears that optimal image hiding conditions are secured when the Wada index stabilizes after the initial decline, the mean of the brightness of the pattern remains stable before dropping down significantly below the average, and the p-value indicates that the distribution becomes Gaussian.

Patterning, From Conifers to Consciousness: Turing’s Theory and Order From Fluctuations

This is a brief account of Turing’s ideas on biological pattern and the events that led to their wider acceptance by biologists as a valid way to investigate developmental pattern, and of the value of theory more generally in biology. Periodic patterns have played a key role in this process, especially 2D arrays of oriented stripes, which proved a disappointment in theoretical terms in the case of Drosophila segmentation, but a boost to theory as applied to skin patterns in fish and model chemical reactions. The concept of “order from fluctuations” is a key component of Turing’s theory, wherein pattern arises by selective amplification of spatial components concealed in the random disorder of molecular and/or cellular processes. For biological examples, a crucial point from an analytical standpoint is knowing the nature of the fluctuations, where the amplifier resides, and the timescale over which selective amplification occurs. The answer clarifies the difference between “inelegant” examples such as Drosophila segmentation, which is perhaps better understood as a programmatic assembly process, and “elegant” ones expressible in equations like Turing’s: that the fluctuations and selection process occur predominantly in evolutionary time for the former, but in real time for the latter, and likewise for error suppression, which for Drosophila is historical, in being lodged firmly in past evolutionary events. The prospects for a further extension of Turing’s ideas to the complexities of brain development and consciousness is discussed, where a case can be made that it could well be in neuroscience that his ideas find their most important application.

The roles of inter-tissue adhesion in development and morphological evolution

The study of how neighboring tissues physically interact with each other, inter-tissue adhesion, is an emerging field at the interface of cell biology, biophysics and developmental biology. Inter-tissue adhesion can be mediated by either cell-extracellular matrix adhesion or cell-cell adhesion, and both the mechanisms and consequences of inter-tissue adhesion have been studied in vivo in numerous vertebrate and invertebrate species. In this Review, we discuss recent progress in understanding the many functions of inter-tissue adhesion in development and evolution. Inter-tissue adhesion can couple the motion of adjacent tissues, be the source of mechanical resistance that constrains morphogenesis, and transmit tension required for normal development. Tissue-tissue adhesion can also create mechanical instability that leads to tissue folding or looping. Transient inter-tissue adhesion can facilitate tissue invasion, and weak tissue adhesion can generate friction that shapes and positions tissues within the embryo. Lastly, we review studies that reveal how inter-tissue adhesion contributes to the diversification of animal morphologies.

Turing Instability and Spatiotemporal Pattern Formation Induced by Nonlinear Reaction Cross-Diffusion in a Predator–Prey System with Allee Effect

The Allee effect is widespread among endangered plants and animals in ecosystems, suggesting that a minimum population density or size is necessary for population survival. This paper investigates the stability and pattern formation of a predator–prey model with nonlinear reactive cross-diffusion under Neumann boundary conditions, which introduces the Allee effect. Firstly, the ODE system is asymptotically stable for its positive equilibrium solution. In a reaction system with self-diffusion, the Allee effect can destabilize the system. Then, in a reaction system with cross-diffusion, through a linear stability analysis, the cross-diffusion coefficient is used as a bifurcation parameter, and instability conditions driven by the cross-diffusion are obtained. Furthermore, we show that the system (5) has at least one inhomogeneous stationary solution. Finally, our theoretical results are illustrated with numerical simulations.

Size matters: tissue size as a marker for a transition between reaction-diffusion regimes in spatio-temporal distribution of morphogens

The reaction-diffusion model constitutes one of the most influential mathematical models to study distribution of morphogens in tissues. Despite its widespread use, the effect of finite tissue size on model-predicted spatio-temporal morphogen distributions has not been completely elucidated. In this study, we analytically investigated the spatio-temporal distributions of morphogens predicted by a reaction-diffusion model in a finite one-dimensional domain, as a proxy for a biological tissue, and compared it with the solution of the infinite-domain model. We explored the reduced parameter, the tissue length in units of a characteristic reaction-diffusion length, and identified two reaction-diffusion regimes separated by a crossover tissue size estimated in approximately three characteristic reaction-diffusion lengths. While above this crossover the infinite-domain model constitutes a good approximation, it breaks below this crossover, whereas the finite-domain model faithfully describes the entire parameter space. We evaluated whether the infinite-domain model renders accurate estimations of diffusion coefficients when fitted to finite spatial profiles, a procedure typically followed in fluorescence recovery after photobleaching (FRAP) experiments. We found that the infinite-domain model overestimates diffusion coefficients when the domain is smaller than the crossover tissue size. Thus, the crossover tissue size may be instrumental in selecting the suitable reaction-diffusion model to study tissue morphogenesis.

Persistent homology and the shape of evolutionary games

For nearly three decades, spatial games have produced a wealth of insights to the study of behavior and its relation to population structure. However, as different rules and factors are added or altered, the dynamics of spatial models often become increasingly complicated to interpret. To tackle this problem, we introduce persistent homology as a rigorous framework that can be used to both define and compute higher-order features of data in a manner which is invariant to parameter choices, robust to noise, and independent of human observation. Our work demonstrates its relevance for spatial games by showing how topological features of simulation data that persist over different spatial scales reflect the stability of strategies in 2D lattice games. To do so, we analyze the persistent homology of scenarios from two games: a Prisoner's Dilemma and a SIRS epidemic model. The experimental results show how the method accurately detects features that correspond to real aspects of the game dynamics. Unlike other tools that study dynamics of spatial systems, persistent homology can tell us something meaningful about population structure while remaining neutral about the underlying structure itself. Regardless of game complexity, since strategies either succeed or fail to conform to shapes of a certain topology there is much potential for the method to provide novel insights for a wide variety of spatially extended systems in biology, social science, and physics.

Coupling Turing stripes to active flows

We numerically solve the active nematohydrodynamic equations of motion, coupled to a Turing reaction-diffusion model, to study the effect of active nematic flow on the stripe patterns resulting from a Turing instability. If the activity is uniform across the system, the Turing patterns dissociate when the flux from active advection balances that from the reaction-diffusion process. If the activity is coupled to the concentration of Turing morphogens, and neighbouring stripes have equal and opposite activity, the system self organises into a pattern of shearing flows, with stripes tending to fracture and slip sideways to join their neighbours. We discuss the role of active instabilities in controlling the crossover between these limits. Our results are of relevance to mechanochemical coupling in biological systems.

Cell Systems Bioelectricity: How Different Intercellular Gap Junctions Could Regionalize a Multicellular Aggregate

Electric potential distributions can act as instructive pre-patterns for development, regeneration, and tumorigenesis in cell systems. The biophysical states influence transcription, proliferation, cell shape, migration, and differentiation through biochemical and biomechanical downstream transduction processes. A major knowledge gap is the origin of spatial patterns in vivo, and their relationship to the ion channels and the electrical synapses known as gap junctions. Understanding this is critical for basic evolutionary developmental biology as well as for regenerative medicine. We computationally show that cells may express connexin proteins with different voltage-gated gap junction conductances as a way to maintain multicellular regions at distinct membrane potentials. We show that increasing the multicellular connectivity via enhanced junction function does not always contribute to the bioelectrical normalization of abnormally depolarized multicellular patches. From a purely electrical junction view, this result suggests that the reduction rather than the increase of specific connexin levels can also be a suitable bioelectrical approach in some cases and time stages. We offer a minimum model that incorporates effective conductances ultimately related to specific ion channel and junction proteins that are amenable to external regulation. We suggest that the bioelectrical patterns and their encoded instructive information can be externally modulated by acting on the mean fields of cell systems, a complementary approach to that of acting on the molecular characteristics of individual cells. We believe that despite the limitations of a biophysically focused model, our approach can offer useful qualitative insights into the collective dynamics of cell system bioelectricity.

Self-Organization of Cellular Units

The purpose of this review is to explore self-organizing mechanisms that pattern microtubules (MTs) and spatially organize animal cell cytoplasm, inspired by recent experiments in frog egg extract. We start by reviewing conceptual distinctions between self-organizing and templating mechanisms for subcellular organization. We then discuss self-organizing mechanisms that generate radial MT arrays and cell centers in the absence of centrosomes. These include autocatalytic MT nucleation, transport of minus ends, and nucleation from organelles such as melanosomes and Golgi vesicles that are also dynein cargoes. We then discuss mechanisms that partition the cytoplasm in syncytia, in which multiple nuclei share a common cytoplasm, starting with cytokinesis, when all metazoan cells are transiently syncytial. The cytoplasm of frog eggs is partitioned prior to cytokinesis by two self-organizing modules, protein regulator of cytokinesis 1 (PRC1)-kinesin family member 4A (KIF4A) and chromosome passenger complex (CPC)-KIF20A. Similar modules may partition longer-lasting syncytia, such as early Drosophila embryos. We end by discussing shared mechanisms and principles for the MT-based self-organization of cellular units.