Towards a physical understanding of developmental patterning

Molecular mechanisms of precise timing in cell lysis

Many biological systems exhibit precise timing of events, and one of the most known examples is cell lysis, which is a process of breaking bacterial host cells in the virus infection cycle. However, the underlying microscopic picture of precise timing remains not well understood. We present a novel theoretical approach to explain the molecular mechanisms of effectively deterministic dynamics in biological systems. Our hypothesis is based on the idea of stochastic coupling between relevant underlying biophysical and biochemical processes that lead to noise cancellation. To test this hypothesis, we introduced a minimal discrete-state stochastic model to investigate how holin proteins produced by bacteriophages break the inner membranes of gram-negative bacteria. By explicitly solving this model, the dynamic properties of cell lysis are fully evaluated, and theoretical predictions quantitatively agree with available experimental data for both wild-type and holin mutants. It is found that the observed threshold-like behavior is a result of the balance between holin proteins entering the membrane and leaving the membrane during the lysis. Theoretical analysis suggests that the cell lysis achieves precise timing for wild-type species by maximizing the number of holins in the membrane and narrowing their spatial distribution. In contrast, for mutated species, these conditions are not satisfied. Our theoretical approach presents a possible molecular picture of precise dynamic regulation in intrinsically random biological processes.

Substrate Rigidity Modulates Segmentation Clock Dynamics in Isolated Presomitic Mesoderm Cells

The segmentation clock, a genetic oscillator in the presomitic mesoderm (PSM), is known to be influenced by biochemical signals, yet its potential regulation by mechanical cues remains unclear. The complex PSM microenvironment has made it challenging to isolate the effects of mechanical perturbations on clock behavior. Here we investigated how mechanical stimuli affect clock oscillations by culturing zebrafish PSM cells on PDMS micropost arrays with tunable rigidities (0.6-1200 kPa). We observed an inverse sigmoidal relationship between surface rigidity and both the percentage of oscillating cells and the number of oscillation cycles, with a switching threshold between 3-6 kPa. The periods of oscillating cells showed a consistently broad distribution across rigidity changes. Moreover, these cells exhibited distinct biophysical properties, such as reduced motility, contractility, and sustained circularity. These findings highlight the crucial role of cell-substrate interactions in regulating segmentation clock behavior, providing insights into the mechanobiology of somitogenesis.

3D reconstruction of the mouse cochlea from scRNA-seq data suggests morphogen-based principles in apex-to-base specification

In the mammalian auditory system, frequency discrimination depends on numerous morphological and physiological properties of the organ of Corti, which gradually change along the apex-to-base (tonotopic) axis of the organ. For example, the basilar membrane stiffness changes tonotopically, thus affecting the tuning properties of individual hair cells. At the molecular level, those frequency-specific characteristics are mirrored by gene expression gradients; however, the molecular mechanisms controlling tonotopic gene expression in the mouse cochlea remain elusive. Through analyzing single-cell RNA sequencing (scRNA-seq) data from E12.5 and E14.5 time points, we predicted that morphogens, rather than a cell division-associated mechanism, confer spatial identity in the extending cochlea. Subsequently, we reconstructed the developing cochlea in 3D space from scRNA-seq data to investigate the molecular pathways mediating positional information. The retinoic acid (RA) and hedgehog pathways were found to form opposing apex-to-base gradients, and functional interrogation using mouse cochlear explants suggested that both pathways jointly specify the longitudinal axis.

Poissonian Cellular Potts Models Reveal Nonequilibrium Kinetics of Cell Sorting

Cellular Potts models are broadly applied across developmental biology and cancer research. We overcome limitations of the traditional approach, which reinterprets a modified Metropolis sampling as ad hoc dynamics, by introducing a physical timescale through Poissonian kinetics and by applying principles of stochastic thermodynamics to separate thermal and relaxation effects from athermal noise and nonconservative forces. Our method accurately describes cell-sorting dynamics in mouse-embryo development and identifies the distinct contributions of nonequilibrium processes, e.g., cell growth and active fluctuations.

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.

Evolution of patterning

Developing tissues are patterned in space and time; this enables them to differentiate their cell types and form complex structures to support different body plans. Although space and time are two independent entities, there are many examples of spatial patterns that originate from temporal ones. The most prominent example is the expression of the genes hunchback, Krüppel, pdm, and castor, which are expressed temporally in the neural stem cells of the Drosophila ventral nerve cord and spatially along the anteroposterior axis of the blastoderm stage embryo. In this Viewpoint, we investigate the relationship between space and time in specific examples of spatial and temporal patterns with the aim of gaining insight into the evolutionary history of patterning.

Bioelectricity in Developmental Patterning and Size Control: Evidence and Genetically Encoded Tools in the Zebrafish Model

Developmental patterning is essential for regulating cellular events such as axial patterning, segmentation, tissue formation, and organ size determination during embryogenesis. Understanding the patterning mechanisms remains a central challenge and fundamental interest in developmental biology. Ion-channel-regulated bioelectric signals have emerged as a player of the patterning mechanism, which may interact with morphogens. Evidence from multiple model organisms reveals the roles of bioelectricity in embryonic development, regeneration, and cancers. The Zebrafish model is the second most used vertebrate model, next to the mouse model. The zebrafish model has great potential for elucidating the functions of bioelectricity due to many advantages such as external development, transparent early embryogenesis, and tractable genetics. Here, we review genetic evidence from zebrafish mutants with fin-size and pigment changes related to ion channels and bioelectricity. In addition, we review the cell membrane voltage reporting and chemogenetic tools that have already been used or have great potential to be implemented in zebrafish models. Finally, new perspectives and opportunities for bioelectricity research with zebrafish are discussed.

Actomyosin pulsing rescues embryonic tissue folding from disruption by myosin fluctuations

During early development, myosin II mechanically reshapes and folds embryo tissue. A much-studied example is ventral furrow formation in Drosophila , marking the onset of gastrulation. Furrowing is driven by contraction of actomyosin networks on apical cell surfaces, but how the myosin patterning encodes tissue shape is unclear, and elastic models failed to reproduce essential features of experimental cell contraction profiles. The myosin patterning exhibits substantial cell-to-cell fluctuations with pulsatile time-dependence, a striking but unexplained feature of morphogenesis in many organisms. Here, using biophysical modeling we find viscous forces offer the principle resistance to actomyosin-driven apical constriction. In consequence, tissue shape is encoded in the direction-dependent curvature of the myosin patterning which orients an anterior-posterior furrow. Tissue contraction is highly sensitive to cell-to-cell myosin fluctuations, explaining furrowing failure in genetically perturbed embryos whose fluctuations are temporally persistent. In wild-type embryos, this catastrophic outcome is averted by pulsatile myosin time-dependence, a time-averaging effect that rescues furrowing. This low pass filter mechanism may underlie the usage of actomyosin pulsing in diverse morphogenetic processes across many organisms.

MEIS1 Is a Common Transcription Repressor of the miR-23a and NORHA Axis in Granulosa Cells

MicroRNA-23a (miR-23a) is an endogenous small activating RNA (saRNA) involved in ovarian granulosa cell (GC) apoptosis and sow fertility by activating lncRNA NORHA transcription. Here, we reported that both miR-23a and NORHA were repressed by a common transcription factor MEIS1, which forms a small network regulating sow GC apoptosis. We characterized the pig miR-23a core promoter, and the putative binding sites of 26 common transcription factors were detected in the core promoters of both miR-23a and NORHA. Of them, transcription factor MEIS1 expression was the highest in the ovary, and widely distributed in various ovarian cells, including GCs. Functionally, MEIS1 is involved in follicular atresia by inhibiting GC apoptosis. Luciferase reporter and ChIP assays showed that transcription factor MEIS1 represses the transcription activity of miR-23a and NORHA through direct binding to their core promoters. Furthermore, MEIS1 represses miR-23a and NORHA expression in GCs. Additionally, MEIS1 inhibits the expression of FoxO1, a downstream of the miR-23a/NORHA axis, and GC apoptosis by repressing the miR-23a/NORHA axis. Overall, our findings point to MEIS1 as a common transcription repressor of miR-23a and NORHA, and develop the miR-23a/NORHA axis into a small regulatory network regulating GC apoptosis and female fertility.

Stem Cells and the Microenvironment: Reciprocity with Asymmetry in Regenerative Medicine

Much of the current research in regenerative medicine concentrates on stem-cell therapy that exploits the regenerative capacities of stem cells when injected into different types of human tissues. Although new therapeutic paths have been opened up by induced pluripotent cells and human mesenchymal cells, the rate of success is still low and mainly due to the difficulties of managing cell proliferation and differentiation, giving rise to non-controlled stem cell differentiation that ultimately leads to cancer. Despite being still far from becoming a reality, these studies highlight the role of physical and biological constraints (e.g., cues and morphogenetic fields) placed by tissue microenvironment on stem cell fate. This asks for a clarification of the coupling of stem cells and microenvironmental factors in regenerative medicine. We argue that extracellular matrix and stem cells have a causal reciprocal and asymmetric relationship in that the 3D organization and composition of the extracellular matrix establish a spatial, temporal, and mechanical control over the fate of stem cells, which enable them to interact and control (as well as be controlled by) the cellular components and soluble factors of microenvironment. Such an account clarifies the notions of stemness and stem cell regeneration consistently with that of microenvironment.

Signaling oscillations in embryonic development

Tight spatiotemporal control of cellular behavior and cell fate decisions is paramount to the formation of multicellular organisms during embryonic development. Intercellular communication via signaling pathways mediates this control. Interestingly, these signaling pathways are not static, but dynamic and change in activity over time. Signaling oscillations as a specific type of dynamics are found in various signaling pathways and model systems. Functions of oscillations include the regulation of periodic events or the transmission of information by encoding signals in the dynamic properties of a signaling pathway. For instance, signaling oscillations in neural or pancreatic progenitor cells modulate their proliferation and differentiation. Oscillations between neighboring cells can also be synchronized, leading to the emergence of waves traveling through the tissue. Such population-wide signaling oscillations regulate for example the consecutive segmentation of vertebrate embryos, a process called somitogenesis. Here, we outline our current understanding of signaling oscillations in embryonic development, how signaling oscillations are generated, how they are studied and how they contribute to the regulation of embryonic development.

Condensation of the Drosophila nerve cord is oscillatory and depends on coordinated mechanical interactions

During development, organs reach precise shapes and sizes. Organ morphology is not always obtained through growth; a classic counterexample is the condensation of the nervous system during Drosophila embryogenesis. The mechanics underlying such condensation remain poorly understood. Here, we characterize the condensation of the embryonic ventral nerve cord (VNC) at both subcellular and tissue scales. This analysis reveals that condensation is not a unidirectional continuous process but instead occurs through oscillatory contractions. The VNC mechanical properties spatially and temporally vary, and forces along its longitudinal axis are spatially heterogeneous. We demonstrate that the process of VNC condensation is dependent on the coordinated mechanical activities of neurons and glia. These outcomes are consistent with a viscoelastic model of condensation, which incorporates time delays and effective frictional interactions. In summary, we have defined the progressive mechanics driving VNC condensation, providing insights into how a highly viscous tissue can autonomously change shape and size.

Cellular Sensing Governs the Stability of Chemotactic Fronts

In contexts ranging from embryonic development to bacterial ecology, cell populations migrate chemotactically along self-generated chemical gradients, often forming a propagating front. Here, we theoretically show that the stability of such chemotactic fronts to morphological perturbations is determined by limitations in the ability of individual cells to sense and thereby respond to the chemical gradient. Specifically, cells at bulging parts of a front are exposed to a smaller gradient, which slows them down and promotes stability, but they also respond more strongly to the gradient, which speeds them up and promotes instability. We predict that this competition leads to chemotactic fingering when sensing is limited at too low chemical concentrations. Guided by this finding and by experimental data on E. coli chemotaxis, we suggest that the cells' sensory machinery might have evolved to avoid these limitations and ensure stable front propagation. Finally, as sensing of any stimuli is necessarily limited in living and active matter in general, the principle of sensing-induced stability may operate in other types of directed migration such as durotaxis, electrotaxis, and phototaxis.

Waves in Embryonic Development

Embryonic development hinges on effective coordination of molecular events across space and time. Waves have recently emerged as constituting an ubiquitous mechanism that ensures rapid spreading of regulatory signals across embryos, as well as reliable control of their patterning, namely, for the emergence of body plan structures. In this article, we review a selection of recent quantitative work on signaling waves and present an overview of the theory of waves. Our aim is to provide a succinct yet comprehensive guiding reference for the theoretical frameworks by which signaling waves can arise in embryos. We start, then, from reaction-diffusion systems, both static and time dependent; move to excitable dynamics; and conclude with systems of coupled oscillators. We link these theoretical models to molecular mechanisms recently elucidated for the control of mitotic waves in early embryos, patterning of the vertebrate body axis, micropattern cultures, and bone regeneration. Our goal is to inspire experimental work that will advance theory in development and connect its predictions to quantitative biological observations. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.