Theory of mechanochemical patterning in biphasic biological tissues

A computational pipeline for spatial mechano-transcriptomics

Advances in spatial profiling technologies are providing insights into how molecular programs are influenced by local signaling and environmental cues. However, cell fate specification and tissue patterning involve the interplay of biochemical and mechanical feedback. Here we develop a computational framework that enables the joint statistical analysis of transcriptional and mechanical signals in the context of spatial transcriptomics. To illustrate the application and utility of the approach, we use spatial transcriptomics data from the developing mouse embryo to infer the forces acting on individual cells, and use these results to identify mechanical, morphometric and gene expression signatures that are predictive of tissue compartment boundaries. In addition, we use geoadditive structural equation modeling to identify gene modules that predict the mechanical behavior of cells in an unbiased manner. This computational framework is easily generalized to other spatial profiling contexts, providing a generic scheme for exploring the interplay of biomolecular and mechanical cues in tissues.

Mechanochemical dynamics of collective cells and hierarchical topological defects in multicellular lumens

Collective cell dynamics is essential for tissue morphogenesis and various biological functions. However, it remains incompletely understood how mechanical forces and chemical signaling are integrated to direct collective cell behaviors underlying tissue morphogenesis. Here, we propose a three-dimensional (3D) mechanochemical theory accounting for biochemical reaction-diffusion and cellular mechanotransduction to investigate the dynamics of multicellular lumens. We show that the interplay between biochemical signaling and mechanics can trigger either pitchfork or Hopf bifurcation to induce diverse static mechanochemical patterns or generate oscillations with multiple modes both involving marked mechanical deformations in lumens. We uncover the crucial role of mechanochemical feedback in emerging morphodynamics and identify the evolution and morphogenetic functions of hierarchical topological defects including cell-level hexatic defects and tissue-level orientational defects. Our theory captures the common mechanochemical traits of collective dynamics observed in experiments and could provide a mechanistic context for understanding morphological symmetry breaking in 3D lumen-like tissues.

Pulsating Active Matter

We reveal that the mechanical pulsation of locally synchronized particles is a generic route to propagate deformation waves. We consider a model of dense repulsive particles whose activity drives periodic change in size of each individual. The dynamics is inspired by biological tissues where cells consume fuel to sustain active deformation. We show that the competition between repulsion and synchronization triggers an instability which promotes a wealth of dynamical patterns, ranging from spiral waves to defect turbulence. We identify the mechanisms underlying the emergence of patterns, and characterize the corresponding transitions. By coarse-graining the dynamics, we propose a hydrodynamic description of an assembly of pulsating particles, and discuss an analogy with reaction-diffusion systems.

Physical interactions in non-ideal fluids promote Turing patterns

Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the inhibiting species, and the involved reactions are highly nonlinear. Such reactions can originate from cooperativity, whose physical interactions should also affect diffusion. We here take direct interactions into account and show that they strongly affect Turing patterns. We find that weak repulsion between the activator and inhibitor can substantially lower the required differential diffusivity and reaction nonlinearity. By contrast, strong interactions can induce phase separation, but the resulting length scale is still typically governed by the fundamental reaction-diffusion length scale. Taken together, our theory connects traditional Turing patterns with chemically active phase separation, thus describing a wider range of systems. Moreover, we demonstrate that even weak interactions affect patterns substantially, so they should be incorporated when modelling realistic systems.

Emergence of Spatial Scales and Macroscopic Tissue Dynamics in Active Epithelial Monolayers

Migrating cells in tissues are often known to exhibit collective swirling movements. In this paper, we develop an active vertex model with polarity dynamics based on contact inhibition of locomotion (CIL). We show that under this dynamics, the cells form steady-state vortices in velocity, polarity, and cell stress with length scales that depend on polarity alignment rate (ζ), self-motility (v0), and cell-cell bond tension (λ). When the ratio λ/v0 becomes larger, the tissue reaches a near jamming state because of the inability of the cells to exchange their neighbors, and the length scale associated with tissue kinematics increases. A deeper examination of this jammed state provides insights into the mechanism of sustained swirl formation under CIL rule that is governed by the feedback between cell polarities and deformations. To gain additional understanding of how active forcing governed by CIL dynamics leads to large-scale tissue dynamics, we systematically coarse-grain cell stress, polarity, and motility and show that the tissue remains polar even on larger length scales. Overall, we explore the origin of swirling patterns during collective cell migration and obtain a connection between cell-level dynamics and large-scale cellular flow patterns observed in epithelial monolayers.

Complex Network Evolution Model Based on Turing Pattern Dynamics

Complex network models are helpful to explain the evolution rules of network structures, and also are the foundations of understanding and controlling complex networks. The existing studies (e.g., scale-free model, small-world model) are insufficient to uncover the internal mechanisms of the emergence and evolution of communities in networks. To overcome the above limitation, in consideration of the fact that a network can be regarded as a pattern composed of communities, we introduce Turing pattern dynamic as theory support to construct the network evolution model. Specifically, we develop a Reaction-Diffusion model according to Q-Learning technology (RDQL), in which each node regarded as an intelligent agent makes a behavior choice to update its relationships, based on the utility and behavioral strategy at every time step. Extensive experiments indicate that our model not only reveals how communities form and evolve, but also can generate networks with the properties of scale-free, small-world and assortativity. The effectiveness of the RDQL model has also been verified by its application in real networks. Furthermore, the depth analysis of the RDQL model provides a conclusion that the proportion of exploration and exploitation behaviors of nodes is the only factor affecting the formation of communities. The proposed RDQL model has potential to be the basic theoretical tool for studying network stability and dynamics.

Tissue interplay during morphogenesis

The process by which biological systems such as cells, tissues and organisms acquire shape has been named as morphogenesis and it is central to a plethora of biological contexts including embryo development, wound healing, or even cancer. Morphogenesis relies in both self-organising properties of the system and in environmental inputs (biochemical and biophysical). The classical view of morphogenesis is based on the study of external biochemical molecules, such as morphogens. However, recent studies are establishing that the mechanical environment is also used by cells to communicate within tissues, suggesting that this mechanical crosstalk is essential to synchronise morphogenetic transitions and self-organisation. In this article we discuss how tissue interaction drive robust morphogenesis, starting from a classical biochemical view, to finalise with more recent advances on how the biophysical properties of a tissue feedback with their surroundings to allow form acquisition. We also comment on how in silico models aid to integrate and predict changes in cell and tissue behaviour. Finally, considering recent advances from the developmental biomechanics field showing that mechanical inputs work as cues that promote morphogenesis, we invite to revisit the concept of morphogen.

A self-generated Toddler gradient guides mesodermal cell migration

The sculpting of germ layers during gastrulation relies on the coordinated migration of progenitor cells, yet the cues controlling these long-range directed movements remain largely unknown. While directional migration often relies on a chemokine gradient generated from a localized source, we find that zebrafish ventrolateral mesoderm is guided by a self-generated gradient of the initially uniformly expressed and secreted protein Toddler/ELABELA/Apela. We show that the Apelin receptor, which is specifically expressed in mesodermal cells, has a dual role during gastrulation, acting as a scavenger receptor to generate a Toddler gradient, and as a chemokine receptor to sense this guidance cue. Thus, we uncover a single receptor-based self-generated gradient as the enigmatic guidance cue that can robustly steer the directional migration of mesoderm through the complex and continuously changing environment of the gastrulating embryo.

Interplay between cell height variations and planar pulsations in epithelial monolayers

Biological tissues change their shapes through collective interactions of cells. This coordination sets length and time scales for dynamics where precision is essential, in particular during morphogenetic events. However, how these scales emerge remains unclear. Here, we address this question using the pulsatile domains observed in confluent epithelial MDCK monolayers where cells exhibit synchronous contraction and extension cycles of [Formula: see text] h duration and [Formula: see text] length scale. We report that the monolayer thickness changes gradually in space and time by more than twofold in order to counterbalance the contraction and extension of the incompressible cytoplasm. We recapitulate these pulsatile dynamics using a continuum model and show that incorporation of cell stiffness dependent height variations is critical both for generating temporal pulsations and establishing the domain size. We propose that this feedback between height and mechanics could be important in coordinating the length scales of tissue dynamics.

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.

Systems of pattern formation within developmental biology

Applications of mathematical models to developmental biology have provided helpful insight into various subfields, ranging from the patterning of animal skin to the development of complex organ systems. Systems involved in patterning within morphology present a unique path to explain self-organizing systems. Current efforts show that patterning systems, notably Reaction-Diffusion and specific signaling pathways, provide insight for explaining morphology and could provide novel applications revolving around the formation of biological systems. Furthermore, the application of pattern formation provides a new perspective on understanding developmental biology and pathology research to study molecular mechanisms. The current review is to cover and take a more in-depth overlook at current applications of patterning systems while also building on the principles of patterning of future research in predictive medicine.

Mechanical Patterning in Animal Morphogenesis

Morphogenesis is one of the most remarkable examples of biological pattern formation. Despite substantial progress in the field, we still do not understand the organizational principles responsible for the robust convergence of the morphogenesis process across scales to form viable organisms under variable conditions. Achieving large-scale coordination requires feedback between mechanical and biochemical processes, spanning all levels of organization and relating the emerging patterns with the mechanisms driving their formation. In this review, we highlight the role of mechanics in the patterning process, emphasizing the active and synergistic manner in which mechanical processes participate in developmental patterning rather than merely following a program set by biochemical signals. We discuss the value of applying a coarse-grained approach toward understanding this complex interplay, which considers the large-scale dynamics and feedback as well as complementing the reductionist approach focused on molecular detail. A central challenge in this approach is identifying relevant coarse-grained variables and developing effective theories that can serve as a basis for an integrated framework for understanding this remarkable pattern-formation process. Expected final online publication date for the Annual Review of Cell and Developmental Biology, Volume 37 is October 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Modeling mechanochemical pattern formation in elastic sheets of biological matter

Inspired by active shape morphing in developing tissues and biomaterials, we investigate two generic mechanochemical models where the deformations of a thin elastic sheet are driven by, and in turn affect, the concentration gradients of a chemical signal. We develop numerical methods to study the coupled elastic deformations and chemical concentration kinetics, and illustrate with computations the formation of different patterns depending on shell thickness, strength of mechanochemical coupling and diffusivity. In the first model, the sheet curvature governs the production of a contractility inhibitor and depending on the threshold in the coupling, qualitatively different patterns occur. The second model is based on the stress-dependent activity of myosin motors and demonstrates how the concentration distribution patterns of molecular motors are affected by the long-range deformations generated by them. Since the propagation of mechanical deformations is typically faster than chemical kinetics (of molecular motors or signaling agents that affect motors), we describe in detail and implement a numerical method based on separation of timescales to effectively simulate such systems. We show that mechanochemical coupling leads to long-range propagation of patterns in disparate systems through elastic instabilities even without the diffusive or advective transport of the chemicals.

Turing's Diffusive Threshold in Random Reaction-Diffusion Systems

Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in most systems with N=2 diffusing species, forcing experimental realizations of the instability to rely on fluctuations or additional nondiffusing species. Here, we ask whether this diffusive threshold lowers for N>2 to allow "true" Turing instabilities. Inspired by May's analysis of the stability of random ecological communities, we analyze the probability distribution of the diffusive threshold in reaction-diffusion systems defined by random matrices describing linearized dynamics near a homogeneous fixed point. In the numerically tractable cases N⩽6, we find that the diffusive threshold becomes more likely to be smaller and physical as N increases, and that most of these many-species instabilities cannot be described by reduced models with fewer diffusing species.

From embryos to embryoids: How external signals and self-organization drive embryonic development

Embryonic development has been traditionally seen as an inductive process directed by exogenous maternal inputs and extra-embryonic signals. Increasing evidence, however, is showing that, in addition to exogenous signals, the development of the embryo involves endogenous self-organization. Recently, this self-organizing potential has been highlighted by a number of stem cell models known as embryoids that can recapitulate different aspects of embryogenesis in vitro. Here, we review the self-organizing behaviors observed in different embryoid models and seek to reconcile this new evidence with classical knowledge of developmental biology. This analysis leads to reexamine embryonic development as a guided self-organizing process, where patterning and morphogenesis are controlled by a combination of exogenous signals and endogenous self-organization. Finally, we discuss the multidisciplinary approach required to investigate the genetic and cellular basis of self-organization.

Roadmap for the multiscale coupling of biochemical and mechanical signals during development

The way in which interactions between mechanics and biochemistry lead to the emergence of complex cell and tissue organization is an old question that has recently attracted renewed interest from biologists, physicists, mathematicians and computer scientists. Rapid advances in optical physics, microscopy and computational image analysis have greatly enhanced our ability to observe and quantify spatiotemporal patterns of signalling, force generation, deformation, and flow in living cells and tissues. Powerful new tools for genetic, biophysical and optogenetic manipulation are allowing us to perturb the underlying machinery that generates these patterns in increasingly sophisticated ways. Rapid advances in theory and computing have made it possible to construct predictive models that describe how cell and tissue organization and dynamics emerge from the local coupling of biochemistry and mechanics. Together, these advances have opened up a wealth of new opportunities to explore how mechanochemical patterning shapes organismal development. In this roadmap, we present a series of forward-looking case studies on mechanochemical patterning in development, written by scientists working at the interface between the physical and biological sciences, and covering a wide range of spatial and temporal scales, organisms, and modes of development. Together, these contributions highlight the many ways in which the dynamic coupling of mechanics and biochemistry shapes biological dynamics: from mechanoenzymes that sense force to tune their activity and motor output, to collectives of cells in tissues that flow and redistribute biochemical signals during development.

Rigidity percolation uncovers a structural basis for embryonic tissue phase transitions

Embryo morphogenesis is impacted by dynamic changes in tissue material properties, which have been proposed to occur via processes akin to phase transitions (PTs). Here, we show that rigidity percolation provides a simple and robust theoretical framework to predict material/structural PTs of embryonic tissues from local cell connectivity. By using percolation theory, combined with directly monitoring dynamic changes in tissue rheology and cell contact mechanics, we demonstrate that the zebrafish blastoderm undergoes a genuine rigidity PT, brought about by a small reduction in adhesion-dependent cell connectivity below a critical value. We quantitatively predict and experimentally verify hallmarks of PTs, including power-law exponents and associated discontinuities of macroscopic observables. Finally, we show that this uniform PT depends on blastoderm cells undergoing meta-synchronous divisions causing random and, consequently, uniform changes in cell connectivity. Collectively, our theoretical and experimental findings reveal the structural basis of material PTs in an organismal context.

Interactions at engineered graft-tissue interfaces: A review

The interactions at the graft-tissue interfaces are critical for the results of engraftments post-implantation. To improve the success rate of the implantations, as well as the quality of the patients' life, understanding the possible reactions between artificial materials and the host tissues is helpful in designing new generations of material-based grafts aiming at inducing specific responses from surrounding tissues for their own reparation and regeneration. To help researchers understand the complicated interactions that occur after implantations and to promote the development of better-designed grafts with improved biocompatibility and patient responses, in this review, the topics will be discussed from the basic reactions that occur chronologically at the graft-tissue interfaces after implantations to the existing and potential applications of the mechanisms of such reactions in designing of grafts. It offers a chance to bring up-to-date advances in the field and new strategies of controlling the graft-tissue interfaces.

Engineering Stem Cell Self-organization to Build Better Organoids

Organoids form through self-organization processes in which initially homogeneous populations of stem cells spontaneously break symmetry and undergo in-vivo-like pattern formation and morphogenesis, though the processes controlling this are poorly characterized. While these in vitro self-organized tissues far exceed the microscopic and functional complexity obtained by current tissue engineering technologies, they are non-physiological in shape and size and have limited function and lifespan. Here, we discuss how engineering efforts for guiding stem-cell-based development at multiple stages can form the basis for the assembly of highly complex and rationally designed self-organizing multicellular systems with increased robustness and physiological relevance.

Shaping Organs: Shared Structural Principles Across Kingdoms

Development encapsulates the morphogenesis of an organism from a single fertilized cell to a functional adult. A critical part of development is the specification of organ forms. Beyond the molecular control of morphogenesis, shape in essence entails structural constraints and thus mechanics. Revisiting recent results in biophysics and development, and comparing animal and plant model systems, we derive key overarching principles behind the formation of organs across kingdoms. In particular, we highlight how growing organs are active rather than passive systems and how such behavior plays a role in shaping the organ. We discuss the importance of considering different scales in understanding how organs form. Such an integrative view of organ development generates new questions while calling for more cross-fertilization between scientific fields and model system communities.

Engineering and modeling of multicellular morphologies and patterns

Synthetic multicellular (MC) systems have the capacity to increase our understanding of biofilms and higher organisms, and to serve as engineering platforms for developing complex products in the areas of medicine, biosynthesis and smart materials. Here we provide an interdisciplinary perspective and review on emerging approaches to engineer and model MC systems. We lay out definitions for key terms in the field and identify toolboxes of standardized parts which can be combined into various MC algorithms to achieve specific outcomes. Many essential parts and algorithms have been demonstrated in some form. As key next milestones for the field, we foresee the improvement of these parts and their adaptation to more biological systems, the demonstration of more complex algorithms, the advancement of quantitative modeling approaches and compilers to support rational MC engineering, and implementation of MC engineering for practical applications.

Mechanochemical Feedback Loops in Development and Disease

There is increasing evidence that both mechanical and biochemical signals play important roles in development and disease. The development of complex organisms, in particular, has been proposed to rely on the feedback between mechanical and biochemical patterning events. This feedback occurs at the molecular level via mechanosensation but can also arise as an emergent property of the system at the cellular and tissue level. In recent years, dynamic changes in tissue geometry, flow, rheology, and cell fate specification have emerged as key platforms of mechanochemical feedback loops in multiple processes. Here, we review recent experimental and theoretical advances in understanding how these feedbacks function in development and disease.

Pattern formation mechanisms of self-organizing reaction-diffusion systems

Embryonic development is a largely self-organizing process, in which the adult body plan arises from a ball of cells with initially nearly equal potency. The reaction-diffusion theory first proposed by Alan Turing states that the initial symmetry in embryos can be broken by the interplay between two diffusible molecules, whose interactions lead to the formation of patterns. The reaction-diffusion theory provides a valuable framework for self-organized pattern formation, but it has been difficult to relate simple two-component models to real biological systems with multiple interacting molecular species. Recent studies have addressed this shortcoming and extended the reaction-diffusion theory to realistic multi-component networks. These efforts have challenged the generality of previous central tenets derived from the analysis of simplified systems and guide the way to a new understanding of self-organizing processes. Here, we discuss the challenges in modeling multi-component reaction-diffusion systems and how these have recently been addressed. We present a synthesis of new pattern formation mechanisms derived from these analyses, and we highlight the significance of reaction-diffusion principles for developmental and synthetic pattern formation.

Integration of luminal pressure and signalling in tissue self-organization

Many developmental processes involve the emergence of intercellular fluid-filled lumina. This process of luminogenesis results in a build up of hydrostatic pressure and signalling molecules in the lumen. However, the potential roles of lumina in cellular functions, tissue morphogenesis and patterning have yet to be fully explored. In this Review, we discuss recent findings that describe how pressurized fluid expansion can provide both mechanical and biochemical cues to influence cell proliferation, migration and differentiation. We also review emerging techniques that allow for precise quantification of fluid pressure in vivo and in situ. Finally, we discuss the intricate interplay between luminogenesis, tissue mechanics and signalling, which provide a new dimension for understanding the principles governing tissue self-organization in embryonic development.

On growth and force: mechanical forces in development

The EMBO/EMBL Symposium 'Mechanical Forces in Development' was held in Heidelberg, Germany, on 3-6 July 2019. This interdisciplinary symposium brought together an impressive and diverse line-up of speakers seeking to address the origin and role of mechanical forces in development. Emphasising the importance of integrative approaches and theoretical simulations to obtain comprehensive mechanistic insights into complex morphogenetic processes, the meeting provided an ideal platform to discuss the concepts and methods of developmental mechanobiology in an era of fast technical and conceptual progress. Here, we summarise the concepts and findings discussed during the meeting, as well as the agenda it sets for the future of developmental mechanobiology.

Positional information and tissue scaling during development and regeneration

In order to contribute to the appropriate tissues during development, cells need to know their position within the embryo. This positional information is conveyed by gradients of signaling molecules, termed morphogens, that are produced in specific regions of the embryo and induce concentration-dependent responses in target tissues. Positional information is remarkably robust, and embryos often develop with the correct proportions even if large parts of the embryo are removed. In this Review, we discuss classical embryological experiments and modern quantitative analyses that have led to mechanistic insights into how morphogen gradients adapt, scale and properly pattern differently sized domains. We analyze these experimental findings in the context of mathematical models and synthesize general principles that apply to multiple systems across species and developmental stages.