Positional information and patterning revisited

A mathematical framework for understanding the spontaneous emergence of complexity applicable to growing multicellular systems

In embryonic development and organogenesis, cells sharing identical genetic codes acquire diverse gene expression states in a highly reproducible spatial distribution, crucial for multicellular formation and quantifiable through positional information. To understand the spontaneous growth of complexity, we constructed a one-dimensional division-decision model, simulating the growth of cells with identical genetic networks from a single cell. Our findings highlight the pivotal role of cell division in providing positional cues, escorting the system toward states rich in information. Moreover, we pinpointed lateral inhibition as a critical mechanism translating spatial contacts into gene expression. Our model demonstrates that the spatial arrangement resulting from cell division, combined with cell lineages, imparts positional information, specifying multiple cell states with increased complexity-illustrated through examples in C.elegans. This study constitutes a foundational step in comprehending developmental intricacies, paving the way for future quantitative formulations to construct synthetic multicellular patterns.

Bone morphogenetic protein signaling: the pathway and its regulation

In the mid-1960s, bone morphogenetic proteins (BMPs) were first identified in the extracts of bone to have the remarkable ability to induce heterotopic bone. When the Drosophila gene decapentaplegic (dpp) was first identified to share sequence similarity with mammalian BMP2/BMP4 in the late-1980s, it became clear that secreted BMP ligands can mediate processes other than bone formation. Following this discovery, collaborative efforts between Drosophila geneticists and mammalian biochemists made use of the strengths of their respective model systems to identify BMP signaling components and delineate the pathway. The ability to conduct genetic modifier screens in Drosophila with relative ease was critical in identifying the intracellular signal transducers for BMP signaling and the related transforming growth factor-beta/activin signaling pathway. Such screens also revealed a host of genes that encode other core signaling components and regulators of the pathway. In this review, we provide a historical account of this exciting time of gene discovery and discuss how the field has advanced over the past 30 years. We have learned that while the core BMP pathway is quite simple, composed of 3 components (ligand, receptor, and signal transducer), behind the versatility of this pathway lies multiple layers of regulation that ensures precise tissue-specific signaling output. We provide a sampling of these discoveries and highlight many questions that remain to be answered to fully understand the complexity of BMP signaling.

Spatially Defined Cell-Secreted Protein Detection Using Granular Hydrogels: μGeLISA

Intercellular communication through secreted proteins is necessary in essential processes such as embryo and limb development, disease progression, and immune responses. There exist many techniques to study bulk solution protein concentrations, but there is a limited set of tools to study the concentrations of cell-secreted proteins in situ within diverse cell platforms while retaining spatial information. In this study, we have developed a microgel system that is able to quantitatively measure the cell-secreted protein concentration within defined three-dimensional culture configurations with single-cell spatial resolution, called μGeLISA (microgel-linked immunosorbent assay). This system, which is based on the surface modification of polyethylene glycol microgels, was able to detect interleukin 6 (IL-6) concentrations of 2.21-21.86 ng/mL. Microgels were also able to detect cell spheroid-secreted IL-6 and distinguish between low- and high-secreting single cells. The system was also adapted to measure the concentration of cell-secreted matrix metalloproteinase-2 (MMP-2). μGeLISA represents a highly versatile system with a straightforward fabrication process that can be adapted toward the detection of secreted proteins within a diverse range of cell culture configurations.

Collective gradient sensing with limited positional information

Eukaryotic cells sense chemical gradients to decide where and when to move. Clusters of cells can sense gradients more accurately than individual cells by integrating measurements of the concentration made across the cluster. Is this gradient-sensing accuracy impeded when cells have limited knowledge of their position within the cluster, i.e., limited positional information? We apply maximum likelihood estimation to study gradient-sensing accuracy of a cluster of cells with finite positional information. If cells must estimate their location within the cluster, this lowers the accuracy of collective gradient sensing. We compare our results with a tug-of-war model where cells respond to the gradient by polarizing away from their neighbors without relying on their positional information. As the cell positional uncertainty increases, there is a trade-off where the tug-of-war model responds more accurately to the chemical gradient. However, for sufficiently large cell clusters or sufficiently shallow chemical gradients, the tug-of-war model will always be suboptimal to one that integrates information from all cells, even if positional uncertainty is high.

Establishment and interpretation of NODAL and BMP signaling gradients in early vertebrate development

Transforming growth factor β (TGF-β) family ligands play crucial roles in orchestrating early embryonic development. Most significantly, two family members, NODAL and BMP form signaling gradients and indeed in fish, frogs and sea urchins these two opposing gradients are sufficient to organize a complete embryonic axis. This review focuses on how these gradients are established and interpreted during early vertebrate development. The review highlights key principles that are emerging, in particular the importance of signaling duration as well as ligand concentration in both gradient generation and their interpretation. Feedforward and feedback loops involving other signaling pathways are also essential for providing spatial and temporal information downstream of the NODAL and BMP signaling pathways. Finally, new data suggest the existence of buffering mechanisms, whereby early signaling defects can be readily corrected downstream later in development, suggesting that signaling gradients do not have to be as precise as previously thought.

Smad4 controls signaling robustness and morphogenesis by differentially contributing to the Nodal and BMP pathways

The transcriptional effector SMAD4 is a core component of the TGF-β family signaling pathways. However, its role in vertebrate embryo development remains unresolved. To address this, we deleted Smad4 in zebrafish and investigated the consequences of this on signaling by the TGF-β family morphogens, BMPs and Nodal. We demonstrate that in the absence of Smad4, dorsal/ventral embryo patterning is disrupted due to the loss of BMP signaling. However, unexpectedly, Nodal signaling is maintained, but lacks robustness. This Smad4-independent Nodal signaling is sufficient for mesoderm specification, but not for optimal endoderm specification. Furthermore, using Optical Projection Tomography in combination with 3D embryo morphometry, we have generated a BMP morphospace and demonstrate that Smad4 mutants are morphologically indistinguishable from embryos in which BMP signaling has been genetically/pharmacologically perturbed. Smad4 is thus differentially required for signaling by different TGF-β family ligands, which has implications for diseases where Smad4 is mutated or deleted.

Heterochromatin Networks: Topology, Dynamics, and Function (a Working Hypothesis)

Open systems can only exist by self-organization as pulsing structures exchanging matter and energy with the outer world. This review is an attempt to reveal the organizational principles of the heterochromatin supra-intra-chromosomal network in terms of nonlinear thermodynamics. The accessibility of the linear information of the genetic code is regulated by constitutive heterochromatin (CHR) creating the positional information in a system of coordinates. These features include scale-free splitting-fusing of CHR with the boundary constraints of the nucleolus and nuclear envelope. The analysis of both the literature and our own data suggests a radial-concentric network as the main structural organization principle of CHR regulating transcriptional pulsing. The dynamic CHR network is likely created together with nucleolus-associated chromatin domains, while the alveoli of this network, including springy splicing speckles, are the pulsing transcription hubs. CHR contributes to this regulation due to the silencing position variegation effect, stickiness, and flexible rigidity determined by the positioning of nucleosomes. The whole system acts in concert with the elastic nuclear actomyosin network which also emerges by self-organization during the transcriptional pulsing process. We hypothesize that the the transcriptional pulsing, in turn, adjusts its frequency/amplitudes specified by topologically associating domains to the replication timing code that determines epigenetic differentiation memory.

Morphometric and allometric rules of polyp's landscape in regular and chimeric coral colonies of the branching species Stylophora pistillata

BACKGROUND

Most studies on architectural rules in corals have focused on the branch and the colony level, unveiling a variety of allometric rules. Working on the branching coral Stylophora pistillata, here we further extend the astogenic directives of this species at the polyp level, to reveal allometric and morphometric rules dictating polyps' arrangement.

RESULTS

We identified a basic morphometric landscape as a six-polyp circlet developed around a founder polyp, with established distances between polyps (six equilateral triangles), reflecting a strong genetic-based background vs high plasticity on the population level. Testing these rules in regular and chimeric S. pistillata colonies, we revealed similar morphometric/allometric rules developed via a single astogenic pathway. In regular colonies, this pathway was driven by the presence/absence of intra-circlet budding polyps, while in chimeras, by the distances between the two founder polyps. In addition, we identified the intra-circlet budding as the origin of first branching, if BPC distances are kept <1.09 ± 0.25 mm.

CONCLUSIONS

The emerged allometric/morphometric rules indicate the existence of a positional information paradigm for polyps' landscape distribution, where each polyp creates its own positional field of morphogen gradients through six inductive sites, thus forming six positional fields for the development of the archetypal "six-polyp crown".

To be more precise: the role of intracellular trafficking in development and pattern formation

Living cells interpret a variety of signals in different contexts to elucidate functional responses. While the understanding of signalling molecules, their respective receptors and response at the gene transcription level have been relatively well-explored, how exactly does a single cell interpret a plethora of time-varying signals? Furthermore, how their subsequent responses at the single cell level manifest in the larger context of a developing tissue is unknown. At the same time, the biophysics and chemistry of how receptors are trafficked through the complex dynamic transport network between the plasma membrane-endosome-lysosome-Golgi-endoplasmic reticulum are much more well-studied. How the intracellular organisation of the cell and inter-organellar contacts aid in orchestrating trafficking, as well as signal interpretation and modulation by the cells are beginning to be uncovered. In this review, we highlight the significant developments that have strived to integrate endosomal trafficking, signal interpretation in the context of developmental biology and relevant open questions with a few chosen examples. Furthermore, we will discuss the imaging technologies that have been developed in the recent past that have the potential to tremendously accelerate knowledge gain in this direction while shedding light on some of the many challenges.

Mesoderm patterning by a dynamic gradient of retinoic acid signalling

Retinoic acid (RA), derived from vitamin A, is a major teratogen, clinically recognized in 1983. Identification of its natural presence in the embryo and dissection of its molecular mechanism of action became possible in the animal model with the advent of molecular biology, starting with the cloning of its nuclear receptor. In normal development, the dose of RA is tightly controlled to regulate organ formation. Its production depends on enzymes, which have a dynamic expression profile during embryonic development. As a small molecule, it diffuses rapidly and acts as a morphogen. Here, we review advances in deciphering how endogenously produced RA provides positional information to cells. We compare three mesodermal tissues, the limb, the somites and the heart, and discuss how RA signalling regulates antero-posterior and left-right patterning. A common principle is the establishment of its spatio-temporal dynamics by positive and negative feedback mechanisms and by antagonistic signalling by FGF. However, the response is cell-specific, pointing to the existence of cofactors and effectors, which are as yet incompletely characterized. This article is part of a discussion meeting issue 'Contemporary morphogenesis'.

ERK phosphorylates chromosomal axis component HORMA domain protein HTP-1 to regulate oocyte numbers

Oocyte numbers, a critical determinant of female reproductive fitness, are highly regulated, yet the mechanisms underlying this regulation remain largely undefined. In the Caenorhabditis elegans gonad, RAS/extracellular signal-regulated kinase (ERK) signaling regulates oocyte numbers; mechanisms are unknown. We show that the RAS/ERK pathway phosphorylates meiotic chromosome axis protein HTP-1 at serine-325 to control chromosome dynamics and regulate oocyte number. Phosphorylated HTP-1(S325) accumulates in vivo in an ERK-dependent manner in early-mid pachytene stage germ cells and is necessary for synaptonemal complex extension and/or maintenance. Lack of HTP-1 phosphorylation leads to asynapsis and persistence of meiotic double-strand breaks, causing delayed meiotic progression and reduced oocyte number. In contrast, early onset of ERK activation causes precocious meiotic progression, resulting in increased oocyte number, which is reversed by removal of HTP-1 phosphorylation. The RAS/ERK/HTP-1 signaling cascade thus functions to monitor formation and maintenance of synapsis for timely resolution of double-strand breaks, oocyte production, and reproductive fitness.

Homeoprotein transduction in neurodevelopment and physiopathology

Homeoproteins were originally identified for embryonic cell-autonomous transcription activity, but they also have non-cell-autonomous activity owing to transfer between cells. This Review discusses transfer mechanisms and focuses on some established functions, such as neurodevelopmental regulation of axon guidance, and postnatal critical periods of brain plasticity that affect sensory processing and cognition. Homeoproteins are present across all eukaryotes, and intercellular transfer occurs in plants and animals. Proposed functions have evolutionary relevance, such as morphogenetic activity and sexual exchange during the mating of unicellular eukaryotes, while others have physiopathological relevance, such as regulation of mood and cognition by influencing brain compartmentalization, connectivity, and plasticity. There are more than 250 known homeoproteins with conserved transfer domains, suggesting that this is a common mode of signal transduction but with many undiscovered functions.

The dynamic transmission of positional information in stau- mutants during Drosophila embryogenesis

It has been suggested that Staufen (Stau) is key in controlling the variability of the posterior boundary of the Hb anterior domain (xHb). However, the mechanism that underlies this control is elusive. Here, we quantified the dynamic 3D expression of segmentation genes in Drosophila embryos. With improved control of measurement errors, we show that the xHb of stau- mutants reproducibly moves posteriorly by 10% of the embryo length (EL) to the wild type (WT) position in the nuclear cycle (nc) 14, and that its variability over short time windows is comparable to that of the WT. Moreover, for stau- mutants, the upstream Bicoid (Bcd) gradients show equivalent relative intensity noise to that of the WT in nc12-nc14, and the downstream Even-skipped (Eve) and cephalic furrow (CF) show the same positional errors as these factors in WT. Our results indicate that threshold-dependent activation and self-organized filtering are not mutually exclusive and could both be implemented in early Drosophila embryogenesis.

French flag gradients and Turing reaction-diffusion versus differentiation waves as models of morphogenesis

The Turing reaction-diffusion model and the French Flag Model are widely accepted in the field of development as the best models for explaining embryogenesis. Virtually all current attempts to understand cell differentiation in embryos begin and end with the assumption that some combination of these two models works. The result may become a bias in embryogenesis in assuming the problem has been solved by these two-chemical substance-based models. Neither model is applied consistently. We review the differences between the French Flag, Turing reaction-diffusion model, and a mechanochemical model called the differentiation wave/cell state splitter model. The cytoskeletal cell state splitter and the embryonic differentiation waves was first proposed in 1987 as a combined physics and chemistry model for cell differentiation in embryos, based on empirical observations on urodele amphibian embryos. We hope that the development of theory can be advanced and observations relevant to distinguishing the embryonic differentiation wave model from the French Flag model and reaction-diffusion equations will be taken up by experimentalists. Experimentalists rely on mathematical biologists for theory, and therefore depend on them for what parameters they choose to measure and ignore. Therefore, mathematical biologists need to fully understand the distinctions between these three models.

Noise-driven cell differentiation and the emergence of spatiotemporal patterns

The emergence of phenotypic diversity in a population of cells and their arrangement in space and time is one of the most fascinating features of living systems. In fact, understanding multicellularity is unthinkable without explaining the proximate and the ultimate causes of cell differentiation in time and space. Simpler forms of cell differentiation can be found in unicellular organisms, such as bacterial biofilm, where reversible cell differentiation results in phenotypically diverse populations. In this manuscript, we attempt to start with the simple case of reversible nongenetic phenotypic to construct a model of differentiation and pattern formation. Our model, which we refer to as noise-driven differentiation (NDD) model, is an attempt to consider the prevalence of noise in biological systems, alongside what is known about genetic switches and signaling, to create a simple model which generates spatiotemporal patterns from bottom-up. Our simulations indicate that the presence of noise in cells can lead to reversible differentiation and the addition of signaling can create spatiotemporal pattern.

Temporal dynamics in the formation and interpretation of Nodal and BMP morphogen gradients

One of the most powerful ideas in developmental biology has been that of the morphogen gradient. In the classical view, a signaling molecule is produced at a local source from where it diffuses, resulting in graded levels across the tissue. This gradient provides positional information, with thresholds in the level of the morphogen determining the position of different cell fates. While experimental studies have uncovered numerous potential morphogens in biological systems, it is becoming increasingly apparent that one important feature, not captured in the simple model, is the role of time in both the formation and interpretation of morphogen gradients. We will focus on two members of the transforming growth factor-β family that are known to play a vital role as morphogens in early vertebrate development: the Nodals and the bone morphogenetic proteins (BMPs). Primarily drawing on the early zebrafish embryo, we will show how recent studies have demonstrated the importance of feedback and other interactions that evolve through time, in shaping morphogen gradients. We will further show how rather than simply reading out levels of a morphogen, the duration of ligand exposure can be a crucial determinant of how cells interpret morphogens, in particular through the unfolding of downstream transcriptional events and in their interactions with other pathways.

The N-space Episenome unifies cellular information space-time within cognition-based evolution

Self-referential cellular homeostasis is maintained by the measured assessment of both internal status and external conditions based within an integrated cellular information field. This cellular field attachment to biologic information space-time coordinates environmental inputs by connecting the cellular senome, as the sum of the sensory experiences of the cell, with its genome and epigenome. In multicellular organisms, individual cellular information fields aggregate into a collective information architectural matrix, termed a N-space Episenome, that enables mutualized organism-wide information management. It is hypothesized that biological organization represents a dual heritable system constituted by both its biological materiality and a conjoining N-space Episenome. It is further proposed that morphogenesis derives from reciprocations between these inter-related facets to yield coordinated multicellular growth and development. The N-space Episenome is conceived as a whole cell informational projection that is heritable, transferable via cell division and essential for the synchronous integration of the diverse self-referential cells that constitute holobionts.

Neural control of body-plan axis in regenerating planaria

Control of axial polarity during regeneration is a crucial open question. We developed a quantitative model of regenerating planaria, which elucidates self-assembly mechanisms of morphogen gradients required for robust body-plan control. The computational model has been developed to predict the fraction of heteromorphoses expected in a population of regenerating planaria fragments subjected to different treatments, and for fragments originating from different regions along the anterior-posterior and medio-lateral axis. This allows for a direct comparison between computational and experimental regeneration outcomes. Vector transport of morphogens was identified as a fundamental requirement to account for virtually scale-free self-assembly of the morphogen gradients observed in planarian homeostasis and regeneration. The model correctly describes altered body-plans following many known experimental manipulations, and accurately predicts outcomes of novel cutting scenarios, which we tested. We show that the vector transport field coincides with the alignment of nerve axons distributed throughout the planarian tissue, and demonstrate that the head-tail axis is controlled by the net polarity of neurons in a regenerating fragment. This model provides a comprehensive framework for mechanistically understanding fundamental aspects of body-plan regulation, and sheds new light on the role of the nervous system in directing growth and form.

Developmental cost of leg-regenerated Coccinella septempunctata (Coleoptera: Coccinellidae)

As larval cannibalism is common under intensive rearing conditions, leg regeneration can help ladybugs adapt to the competitive environment, but whether the leg regeneration leads to side effects on development remains unclear. To analyze the potentially developmental cost of leg regeneration, the developmental period and weight of leg-regenerated Coccinella septempunctata were studied in the laboratory. The results showed that, when the time intervals between the emergency of 4th-instar larva and leg amputation increased, the developmental period of leg-regenerated 4th-instar larvae was gradually prolonged. Significantly developmental delay were also examined at prepupal and pupal stages, and various timings of leg amputation affected the periods of leg-regenerated prepupae/pupae similarly. After the leg was amputated at different larval instars, the developmental delay only occurred at the larval instar when the leg was amputated, whereas other larval instars failed to be extended, and the developmental periods of leg-regenerated prepupae/pupae were affected similarly by the instars of leg amputation. Developmental delays possibly resulted in more consumption by leg-regenerated larvae, and then weight gains at prepupal/pupal stages, but different larval instars of leg amputation affected the weight gain similarly. Both the developmental delay (at 4th-instar larval, prepupal and pupal stages) and weight gain (at pupal and adult stages) in complete/bilateral amputation were longer or greater than those in half/unilateral amputation. However, the thoracic locations of leg amputation impacted the developmental delay and weight gain similarly. Our study indicates that although leg regeneration triggers the developmental cost decreasing the competitive superiority or agility, C. septempunctata larvae still choose to completely regenerate the leg to adapt to complex environments. Thus, in order to remain competitive at adult stages, leg-impaired larvae may make an investment tradeoff between leg regeneration and developmental cost.

Positive and negative regulation of Shh signalling in vertebrate retinal development

Cell-to-cell communication is fundamental for embryo development and subsequent tissue homeostasis. This communication is often mediated by a small number of signaling pathways in which a secreted ligand binds to the surface of a target cell, thereby activating signal transduction. In vertebrate neural development, these signaling mechanisms are repeatedly used to obtain different and context-dependent outcomes. Part of the versatility of these communication mechanisms depends on their finely tuned regulation that controls timing, spatial localization, and duration of the signaling. The existence of secreted antagonists, which prevent ligand–receptor interaction, is an efficient mechanism to regulate some of these pathways. The Hedgehog family of signaling proteins, however, activates a pathway that is controlled largely by the positive or negative activity of membrane-bound proteins such as Cdon, Boc, Gas1, or Megalin/LRP2. In this review, we will use the development of the vertebrate retina, from its early specification to neurogenesis, to discuss whether there is an advantage to the use of such regulators, pointing to unresolved or controversial issues.

Emergence of form in embryogenesis

The development of form in an embryo is the result of a series of topological and informational symmetry breakings. We introduce the vector-reaction-diffusion-drift (VRDD) system where the limit cycle of spatial dynamics is morphogen concentrations with Dirac delta-type distributions. This is fundamentally different from the Turing reaction-diffusion system, as VRDD generates system-wide broken symmetry. We developed 'fundamental forms' from spherical blastula with a single organizing axis (rotational symmetry), double axis (mirror symmetry) and triple axis (no symmetry operator in three dimensions). We then introduced dynamics for cell differentiation, where genetic regulatory states are modelled as a finite-state machine (FSM). The state switching of an FSM is based on local morphogen concentrations as epigenetic information that changes dynamically. We grow complicated forms hierarchically in spatial subdomains using the FSM model coupled with the VRDD system. Using our integrated simulation model with four layers (topological, physical, chemical and regulatory), we generated life-like forms such as hydra. Genotype-phenotype mapping was investigated with continuous and jump mutations. Our study can have applications in morphogenetic engineering, soft robotics and biomimetic design.

Professor Lev Beloussov and the birth of morphomechanics

The first explanations of the mechanisms of development of living organisms were proposed in antiquity. At that time two competing ideas existed, about the strict determination of embryonic structures (we call it the "Hippocrates line") and about the possible formation of structures from the unstructured condition ("Aristotle line"). We can trace the opposition between the "Hippocrates line" and "Aristotle line" from antiquity till the present time. At the end of the XIX century, experimental investigation of the mechanisms of integrity of development had started. In the XX century, the "Aristotle line" finds its expression in the Morphogenetic Field Theory of A.G. Gurwitsch, according to which cells of the organism are integrated in an organic whole. Since the 1970s, mechanical forces and tensions have been considered as integral factors of ontogenesis. One of the most productive scientific teams which worked in this area was the laboratory of Professor L.V. Beloussov from the Lomonossov Moscow State University, Russia. In the 1970s, Lev Beloussov and his colleagues discovered the presence of "passive" and "active" (i.e. metabolically-dependent) mechanical stresses in the tissues of developing organisms, their organization and stage-specific patterns. In 1980-1990 s, a lot of experimental data about the role of the patterns of mechanical stresses in morphogenesis and cell differentiation was accumulated. Based on the experimental data, Professor Beloussov and his colleagues developed a theory of the regulation of the development of living organisms on the basis of the interaction of passive and active mechanical stresses (Belousov-Mittenthal Theory), which forms the basis of a new science - morphomechanics.

Bioelectrical control of positional information in development and regeneration: A review of conceptual and computational advances

Positional information describes pre-patterns of morphogenetic substances that alter spatio-temporal gene expression to instruct development of growth and form. A wealth of recent data indicate bioelectrical properties, such as the transmembrane potential (Vmem), are involved as instructive signals in the spatiotemporal regulation of morphogenesis. However, the mechanistic relationships between Vmem and molecular positional information are only beginning to be understood. Recent advances in computational modeling are assisting in the development of comprehensive frameworks for mechanistically understanding how endogenous bioelectricity can guide anatomy in a broad range of systems. Vmem represents an extraordinarily strong electric field (∼1.0 × 106 V/m) active over the thin expanse of the plasma membrane, with the capacity to influence a variety of downstream molecular signaling cascades. Moreover, in multicellular networks, intercellular coupling facilitated by gap junction channels may induce directed, electrodiffusive transport of charged molecules between cells of the network to generate new positional information patterning possibilities and characteristics. Given the demonstrated role of Vmem in morphogenesis, here we review current understanding of how Vmem can integrate with molecular regulatory networks to control single cell state, and the unique properties bioelectricity adds to transport phenomena in gap junction-coupled cell networks to facilitate self-assembly of morphogen gradients and other patterns. Understanding how Vmem integrates with biochemical regulatory networks at the level of a single cell, and mechanisms through which Vmem shapes molecular positional information in multicellular networks, are essential for a deep understanding of body plan control in development, regeneration and disease.

Complexity: the organizing principle at the interface of biological (dis)order

The term complexity means several things to biologists.When qualifying morphological phenotype, on the one hand, it is used to signify the sheer complicatedness of living systems, especially as a result of the multicomponent aspect of biological form. On the other hand, it has been used to represent the intricate nature of the connections between constituents that make up form: a more process-based explanation. In the context of evolutionary arguments, complexity has been defined, in a quantifiable fashion, as the amount of information, an informatic template such as a sequence of nucleotides or amino acids stores about its environment. In this perspective, we begin with a brief review of the history of complexity theory. We then introduce a developmental and an evolutionary understanding of what it means for biological systems to be complex.We propose that the complexity of living systems can be understood through two interdependent structural properties: multiscalarity of interconstituent mechanisms and excitability of the biological materials. The answer to whether a system becomes more or less complex over time depends on the potential for its constituents to interact in novel ways and combinations to give rise to new structures and functions, as well as on the evolution of excitable properties that would facilitate the exploration of interconstituent organization in the context of their microenvironments and macroenvironments.

Combining Turing and 3D vertex models reproduces autonomous multicellular morphogenesis with undulation, tubulation, and branching

This study demonstrates computational simulations of multicellular deformation coupled with chemical patterning in the three-dimensional (3D) space. To address these aspects, we proposes a novel mathematical model, where a reaction–diffusion system is discretely expressed at a single cell level and combined with a 3D vertex model. To investigate complex phenomena emerging from the coupling of patterning and deformation, as an example, we employed an activator–inhibitor system and converted the activator concentration of individual cells into their growth rate. Despite the simplicity of the model, by growing a monolayer cell vesicle, the coupling system provided rich morphological dynamics such as undulation, tubulation, and branching. Interestingly, the morphological variety depends on the difference in time scales between patterning and deformation, and can be partially understood by the intrinsic hysteresis in the activator-inhibitor system with domain growth. Importantly, the model can be applied to 3D multicellular dynamics that couple the reaction–diffusion patterning with various cell behaviors, such as deformation, rearrangement, division, apoptosis, differentiation, and proliferation. Thus, the results demonstrate the significant advantage of the proposed model as well as the biophysical importance of exploring spatiotemporal dynamics of the coupling phenomena of patterning and deformation in 3D space.

A simple mathematical model of cell clustering by chemotaxis

Chemotaxis is the process by which cells and clusters of cells follow chemical signals in order to combine and form larger clusters. The spreading of the chemical signal from any given cell can be modeled using the linear diffusion equation, and the standard equations of motion can be used to determine how a cell, or cluster of cells, moves in response to the chemical signal. The resulting differential equations for the cell locations are integrated through time using the fourth-order Runge-Kutta method. The effect which changing the initial concentration magnitude, diffusion constant and velocity damping parameter has on the shape of the final clusters of cells is investigated and discussed.

Interstitial fluid flow of alveolar primary septa after pneumonectomy

Neoalveolation is known to occur in the remaining lung after pneumonectomy. While compensatory lung growth is a complex process, stretching of the lung tissue appears to be crucial for tissue remodeling. Even a minute shear stress exerted on fibroblasts in the interstitial space is known to trigger cell differentiation into myofibroblast that are essential to building new tissues. We hypothesize that the non-uniform motion of the primary septa due to their heterogeneous mechanical properties under tidal breathing induces a spatially unique interstitial flow and shear stress distribution in the interstitial space. This may in turn trigger pulmonary fibroblast differentiation and neoalveolation. In this study, we developed a theoretical basis for how cyclic motion of the primary septal walls with heterogeneous mechanical properties affects the interstitial flow and shear stress distribution. The velocity field of the interstitial flow was expressed by a Fourier (complex) series and its leading term was considered to induce the basic structure of stress distribution as long as the dominant length scale of heterogeneity is the size of collapsed alveoli. We conclude that the alteration of mechanical properties of the primary septa caused by pneumonectomy can develop a new interstitial flow field, which alters the shear stress distribution. This may trigger the differentiation of resident fibroblasts, which may in turn induce spatially unique neoalveolation in the remaining lung. Our example illustrates that the initial forming of new alveoli about half the size of the original ones.

Scaling of morphogenetic patterns in reaction-diffusion systems

Development of multicellular organisms is commonly associated with the response of individual cells to concentrations of chemical substances called morphogens. Concentration fields of morphogens form a basis for biological patterning and ensure its properties including ability to scale with the size of the organism. While mechanisms underlying the formation of morphogen gradients are reasonably well understood, little is known about processes responsible for their scaling. Here, we perform a formal analysis of scaling for chemical patterns forming in continuous systems. We introduce a quantity representing the sensitivity of systems to changes in their size and use it to analyse scaling properties of patterns forming in a few different systems. Particularly, we consider how scaling properties of morphogen gradients forming in diffusion-decay systems depend on boundary conditions and how the scaling can be improved by passive modulation of morphogens or active transport in the system. We also analyse scaling of morphogenetic signal caused by two opposing gradients and consider scaling properties of patterns forming in activator-inhibitor systems. We conclude with a few possible mechanisms which allow scaling of morphogenetic patterns.

Positional Information and Pattern Formation

The concept of positional information proposes that cells acquire positional values as in a coordinate system, which they interpret by developing in particular ways to give rise to spatial patterns. Some of the best evidence for positional information comes from regeneration experiments, and the patterning of the leg and antenna in Drosophila, and the vertebrate limb. Central problems are how positional information is set up, how it is recorded, and then how it is interpreted by the cells. A number of models have been proposed for the setting up of positional gradients, and most are based on diffusion of a morphogen and its interactions with extracellular molecules; however, diffusion may not be reliable mechanism. There are also mechanisms based on timing. There is no good evidence for the quantitative aspects of any of the proposed gradients and details how they are set up. The way in which a signaling gradient regulates differential gene expression in a concentration-dependent manner also raises several technical and quite difficult issues. A key feature of positional information being the basis for pattern formation is that there is no prepattern in the embryo.

The molecular and cellular signatures of the mouse eminentia thalami support its role as a signalling centre in the developing forebrain

The mammalian eminentia thalami (EmT) (or thalamic eminence) is an embryonic forebrain structure of unknown function. Here, we examined the molecular and cellular properties of the mouse EmT. We first studied mRNA expression of signalling molecules and found that the EmT is a structure, rich in expression of secreted factors, with Wnts being the most abundantly detected. We then examined whether EmT tissue could induce cell fate changes when grafted ectopically. For this, we transplanted EmT tissue from a tau-GFP mouse to the ventral telencephalon of a wild type host, a telencephalic region where Wnt signalling is not normally active but which we showed in culture experiments is competent to respond to Wnts. We observed that the EmT was able to induce in adjacent ventral telencephalic cells ectopic expression of Lef1, a transcriptional activator and a target gene of the Wnt/β-catenin pathway. These Lef1-positive;GFP-negative cells expressed the telencephalic marker Foxg1 but not Ascl1, which is normally expressed by ventral telencephalic cells. These results suggest that the EmT has the capacity to activate Wnt/β-catenin signalling in the ventral telencephalon and to suppress ventral telencephalic gene expression. Altogether, our data support a role of the EmT as a signalling centre in the developing mouse forebrain.

Fgf15 regulates thalamic development by controlling the expression of proneural genes

The establishment of the brain structural complexity requires a precisely orchestrated interplay between extrinsic and intrinsic signals modulating cellular mechanisms to guide neuronal differentiation. However, little is known about the nature of these signals in the diencephalon, a complex brain region that processes and relays sensory and motor information to and from the cerebral cortex and subcortical structures. Morphogenetic signals from brain organizers regulate histogenetic processes such as cellular proliferation, migration, and differentiation. Sonic hedgehog (Shh) in the key signal of the ZLI, identified as the diencephalic organizer. Fgf15, the mouse gene orthologous of human, chick, and zebrafish Fgf19, is induced by Shh signal and expressed in the diencephalic alar plate progenitors during histogenetic developmental stages. This work investigates the role of Fgf15 signal in diencephalic development. In the absence of Fgf15, the complementary expression pattern of proneural genes: Ascl1 and Nng2, is disrupted and the GABAergic thalamic cells do not differentiate; in addition dorsal thalamic progenitors failed to exit from the mitotic cycle and to differentiate into neurons. Therefore, our findings indicate that Fgf15 is the Shh downstream signal to control thalamic regionalization, neurogenesis, and neuronal differentiation by regulating the expression and mutual segregation of neurogenic and proneural regulatory genes.

Lithium-induced developmental anomalies in the spirotrich ciliate Stylonychia lemnae (Ciliophora, Hypotrichida)

Lithium is known to have profound biological effects of varying intensity in different life forms. In the present investigation, the effect of lithium was studied on the spirotrich ciliate Stylonychia lemnae. Lithium treatment brings about quantitative changes in the patterning of ciliary structures in S. lemnae. The dorsal surface of the affected cells develops supernumerary ciliary kineties due to excessive proliferation of the kinetosomes. The ventral surface on the other hand develops fewer than normal cirri formed from reduced numbers of ciliary primordia. The adoral zone of membranelles (AZM) fails to remodel properly as, in certain segments, membranelles become disarranged and misaligned. Lithium-induced changes are transitory as the normal pattern is restored during recovery after the cells are shifted to normal medium, suggesting non-genic regulation of cortical pattern. Lithium also affects the process of cell proliferation as the number of cells undergoing division is negligible as compared to reorganizing cells. The results point to the extremely complex and heterogeneous organization of the cellular cortex (plasma membrane and cytoskeleton) which is capable of exerting autonomous control over the phenotype and cortical pattern.

Genetic control of morphogenesis in Dictyostelium

Cells grow, move, expand, shrink and die in the process of generating the characteristic shapes of organisms. Although the structures generated during development of the social amoeba Dictyostelium discoideum look nothing like the structures seen in metazoan embryogenesis, some of the morphogenetic processes used in their making are surprisingly similar. Recent advances in understanding the molecular basis for directed cell migration, cell type specific sorting, differential adhesion, secretion of matrix components, pattern formation, regulation and terminal differentiation are reviewed. Genes involved in Dictyostelium aggregation, slug formation, and culmination of fruiting bodies are discussed.

Optimizing information flow in small genetic networks. IV. Spatial coupling

We typically think of cells as responding to external signals independently by regulating their gene expression levels, yet they often locally exchange information and coordinate. Can such spatial coupling be of benefit for conveying signals subject to gene regulatory noise? Here we extend our information-theoretic framework for gene regulation to spatially extended systems. As an example, we consider a lattice of nuclei responding to a concentration field of a transcriptional regulator (the input) by expressing a single diffusible target gene. When input concentrations are low, diffusive coupling markedly improves information transmission; optimal gene activation functions also systematically change. A qualitatively different regulatory strategy emerges where individual cells respond to the input in a nearly steplike fashion that is subsequently averaged out by strong diffusion. While motivated by early patterning events in the Drosophila embryo, our framework is generically applicable to spatially coupled stochastic gene expression models.

Mechanical force sensing in tissues

Tissue size, shape, and organization reflect individual cell behaviors such as proliferation, shape change, and movement. Evidence suggests that mechanical signals operate in tandem with biochemical cues to properly coordinate cell behavior and pattern tissues. The objective of this chapter is to present recent evidence demonstrating that forces transmitted between cells act as signals that coordinate cell behavior across tissues. We first briefly summarize molecular and cellular mechanisms by which forces are sensed by cells with an emphasis on forces generated and transmitted by cytoskeletal networks. We then discuss evidence for these mechanisms operating in multicellular contexts to coordinate complex cell and tissue behaviors that occur during embryonic development: specifically growth and morphogenesis.

Coupling intercellular molecular signalling with multicellular deformation for simulating three-dimensional tissue morphogenesis

During morphogenesis, three-dimensional (3D) multicellular structures emerge from biochemical and mechanical interplays among cells. In particular, by organizing their gradient within tissues, the diffusible signalling molecules play an essential role in producing the spatio-temporal patterns of cell status such as the differentiation states. Notably, this biochemical patterning can be dynamically coupled with multicellular deformations by signal-dependent cell activities such as contraction, adhesion, migration, proliferation and apoptosis. However, the mechanism by which these cellular activities mediate the interactions between multicellular deformations and patterning is still unknown. Herein, we propose a novel framework of a 3D vertex model to express molecular signalling among the mechanically deforming cells. By specifying a density of signalling molecules for each cell, we express their transport between neighbouring cells. By simulating signal-dependent epithelial growth, we found various types of tissue morphogenesis such as arrest, expansion, invagination and evagination. In the expansion phase, growth molecules were widely diffused with increasing tissue volume, which diluted the growth molecules in order to support the autonomous suppression of tissue growth. These results indicate that the proposed model successfully expresses 3D multicellular deformations dynamically coupled with biochemical patterning. We expect our proposed model to be a useful tool for predicting new phenomena emerging from mechanochemical coupling in multicellular morphogenesis.

Sexual selection drives the evolution of limb regeneration in Harmonia axyridis (Coleoptera: Coccinellidae)

When Harmonia axyridis larvae were subjected to amputation of a foreleg in the fourth instar, 83% survived and, of these, 75% regenerated the leg during pupation. Regenerators pupated at heavier weights than controls (unoperated) or non-regenerators, and spent longer in pupation. Regenerated males were preferred by females in choice tests and produced more viable progeny than control males. Unregenerated males were less preferred by females, copulated for shorter periods than control males, and reduced female fecundity. Amputation diminished beneficial paternal effects, whether males regenerated or not, resulting in progeny with slower development and smaller adult body mass relative to control paternity. Progeny of unregenerated males had lower survival and body mass, whether male or female, confirming that regeneration was an honest signal of mate quality. When offspring had a foreleg amputated, a regenerated paternity yielded higher survival than control paternity, but similar rates of regeneration, whereas an unregenerated paternity yielded lower rates of survival and leg regeneration than control paternity. Regenerating beetles were twice as likely to be melanic as non-regenerating or control beetles, suggesting pleiotropic effects of melanism on processes involved in regeneration. This is the first report of complete limb regeneration by a holometabolous insect in the pupal stage, and the first example of sexual selection for regenerative capacity.

Positional information, positional error, and readout precision in morphogenesis: a mathematical framework

The concept of positional information is central to our understanding of how cells determine their location in a multicellular structure and thereby their developmental fates. Nevertheless, positional information has neither been defined mathematically nor quantified in a principled way. Here we provide an information-theoretic definition in the context of developmental gene expression patterns and examine the features of expression patterns that affect positional information quantitatively. We connect positional information with the concept of positional error and develop tools to directly measure information and error from experimental data. We illustrate our framework for the case of gap gene expression patterns in the early Drosophila embryo and show how information that is distributed among only four genes is sufficient to determine developmental fates with nearly single-cell resolution. Our approach can be generalized to a variety of different model systems; procedures and examples are discussed in detail.