The effects of Hh morphogen source movement on signaling dynamics

Morphogens of the Hh family trigger gene expression changes in receiving cells in a concentration-dependent manner to regulate their identity, proliferation, death or metabolism, depending on the tissue or organ. This variety of responses relies on a conserved signaling pathway. Its logic includes a negative-feedback loop involving the Hh receptor Ptc. Here, using experiments and computational models we study and compare the different spatial signaling profiles downstream of Hh in several developing Drosophila organs. We show that the spatial distributions of Ptc and the activator transcription factor CiA in wing, antenna and ocellus show similar features, but are markedly different from that in the compound eye. We propose that these two profile types represent two time points along the signaling dynamics, and that the interplay between the spatial displacement of the Hh source in the compound eye and the negative-feedback loop maintains the receiving cells effectively in an earlier stage of signaling. These results show how the interaction between spatial and temporal dynamics of signaling and differentiation processes may contribute to the informational versatility of the conserved Hh signaling pathway.

A coarse-grained approach to model the dynamics of the actomyosin cortex

Background

The dynamics of the actomyosin machinery is at the core of many important biological processes. Several relevant cellular responses such as the rhythmic compression of the cell cortex are governed, at a mesoscopic level, by the nonlinear interaction between actin monomers, actin crosslinkers, and myosin motors. Coarse-grained models are an optimal tool to study actomyosin systems, since they can include processes that occur at long time and space scales, while maintaining the most relevant features of the molecular interactions.

Results

Here, we present a coarse-grained model of a two-dimensional actomyosin cortex, adjacent to a three-dimensional cytoplasm. Our simplified model incorporates only well-characterized interactions between actin monomers, actin crosslinkers and myosin, and it is able to reproduce many of the most important aspects of actin filament and actomyosin network formation, such as dynamics of polymerization and depolymerization, treadmilling, network formation, and the autonomous oscillatory dynamics of actomyosin.

Conclusions

We believe that the present model can be used to study the in vivo response of actomyosin networks to changes in key parameters of the system, such as alterations in the attachment of actin filaments to the cell cortex.

Supplementary Information

The online version contains supplementary material available at (10.1186/s12915-022-01279-2).

Quantitative Approaches to Study Retinal Neurogenesis

The study of the development of the vertebrate retina can be addressed from several perspectives: from a purely qualitative to a more quantitative approach that takes into account its spatio-temporal features, its three-dimensional structure and also the regulation and properties at the systems level. Here, we review the ongoing transition toward a full four-dimensional characterization of the developing vertebrate retina, focusing on the challenges at the experimental, image acquisition, image processing and quantification. Using the developing zebrafish retina, we illustrate how quantitative data extracted from these type of highly dense, three-dimensional tissues depend strongly on the image quality, image processing and algorithms used to segment and quantify. Therefore, we propose that the scientific community that focuses on developmental systems could strongly benefit from a more detailed disclosure of the tools and pipelines used to process and analyze images from biological samples.

FGF2 modulates simultaneously the mode, the rate of division and the growth fraction in cultures of radial glia

Radial glial progenitors in the mammalian developing neocortex have been shown to follow a deterministic differentiation program restricted to an asymmetric-only mode of division. This feature seems incompatible with their well-known ability to increase in number when cultured in vitro, driven by fibroblast growth factor 2 and other mitogenic signals. The changes in their differentiation dynamics that allow this transition from in vivo asymmetric-only division mode to an in vitro self-renewing culture have not been fully characterized. Here, we combine experiments of radial glia cultures with numerical models and a branching process theoretical formalism to show that fibroblast growth factor 2 has a triple effect by simultaneously increasing the growth fraction, promoting symmetric divisions and shortening the length of the cell cycle. These combined effects partner to establish and sustain a pool of rapidly proliferating radial glial progenitors in vitro. We also show that, in conditions of variable proliferation dynamics, the branching process tool outperforms other commonly used methods based on thymidine analogs, such as BrdU and EdU, in terms of accuracy and reliability.

Highlighted Article: When mode and/or rate of division are changing, a branching process, rather than a thymidine analog method, provides temporal resolution, it is more robust and does not interfere with cell homeostasis.

Human-iPSC-Derived Cardiac Stromal Cells Enhance Maturation in 3D Cardiac Microtissues and Reveal Non-cardiomyocyte Contributions to Heart Disease

Cardiomyocytes (CMs) from human induced pluripotent stem cells (hiPSCs) are functionally immature, but this is improved by incorporation into engineered tissues or forced contraction. Here, we showed that tri-cellular combinations of hiPSC-derived CMs, cardiac fibroblasts (CFs), and cardiac endothelial cells also enhance maturation in easily constructed, scaffold-free, three-dimensional microtissues (MTs). hiPSC-CMs in MTs with CFs showed improved sarcomeric structures with T-tubules, enhanced contractility, and mitochondrial respiration and were electrophysiologically more mature than MTs without CFs. Interactions mediating maturation included coupling between hiPSC-CMs and CFs through connexin 43 (CX43) gap junctions and increased intracellular cyclic AMP (cAMP). Scaled production of thousands of hiPSC-MTs was highly reproducible across lines and differentiated cell batches. MTs containing healthy-control hiPSC-CMs but hiPSC-CFs from patients with arrhythmogenic cardiomyopathy strikingly recapitulated features of the disease. Our MT model is thus a simple and versatile platform for modeling multicellular cardiac diseases that will facilitate industry and academic engagement in high-throughput molecular screening.

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Cardiac fibroblasts and endothelial cells induce hiPSC-cardiomyocyte maturation

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CX43 gap junctions form between cardiac fibroblasts and cardiomyocytes

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cAMP-pathway activation contributes to hiPSC-cardiomyocyte maturation

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Patient-derived hiPSC-cardiac fibroblasts cause arrhythmia in microtissues

Dynamic Hh signalling can generate temporal information during tissue patterning

The differentiation of tissues and organs requires that cells exchange information in space and time. Spatial information is often conveyed by morphogens: molecules that disperse across receiving cells to generate signalling gradients. Cells translate such concentration gradients into space-dependent patterns of gene expression and cellular behaviour. But could morphogen gradients also convey developmental time? Here, by investigating the developmental role of Hh on a component of the Drosophila visual system, the ocellar retina, we have discovered that ocellar cells use the non-linear gradient of Hh as a temporal cue, collectively performing the biological equivalent of a mathematical logarithmic transformation. In this way, a morphogen diffusing from a non-moving source is decoded as a wave of differentiating photoreceptors that travels at constant speed throughout the retinal epithelium.

Drug treatment efficiency depends on the initial state of activation in nonlinear pathways

An accurate prediction of the outcome of a given drug treatment requires quantitative values for all parameters and concentrations involved as well as a detailed characterization of the network of interactions where the target molecule is embedded. Here, we present a high-throughput in silico screening of all potential networks of three interacting nodes to study the effect of the initial conditions of the network in the efficiency of drug inhibition. Our study shows that most network topologies can induce multiple dose-response curves, where the treatment has an enhanced, reduced or even no effect depending on the initial conditions. The type of dual response observed depends on how the potential bistable regimes interplay with the inhibition of one of the nodes inside a nonlinear pathway architecture. We propose that this dependence of the strength of the drug on the initial state of activation of the pathway may be affecting the outcome and the reproducibility of drug studies and clinical trials.

Myosin light-chain phosphatase regulates basal actomyosin oscillations during morphogenesis

Contractile actomyosin networks generate forces that drive tissue morphogenesis. Actomyosin contractility is controlled primarily by reversible phosphorylation of the myosin-II regulatory light chain through the action of myosin kinases and phosphatases. While the role of myosin light-chain kinase in regulating contractility during morphogenesis has been largely characterized, there is surprisingly little information on myosin light-chain phosphatase (MLCP) function in this context. Here, we use live imaging of Drosophila follicle cells combined with mathematical modelling to demonstrate that the MLCP subunit flapwing (flw) is a key regulator of basal myosin oscillations and cell contractions underlying egg chamber elongation. Flw expression decreases specifically on the basal side of follicle cells at the onset of contraction and flw controls the initiation and periodicity of basal actomyosin oscillations. Contrary to previous reports, basal F-actin pulsates similarly to myosin. Finally, we propose a quantitative model in which periodic basal actomyosin oscillations arise in a cell-autonomous fashion from intrinsic properties of motor assemblies.

Actomyosin contractility is regulated by phosphorylation of myosin regulatory light chain; much of the work in this area has focused on the kinase. Here the authors use Drosophila follicle cells and modelling to show that the phosphatase subunit Flapwing controls the initiation and dynamics of actomyosin oscillations.

A Branching Process to Characterize the Dynamics of Stem Cell Differentiation

The understanding of the regulatory processes that orchestrate stem cell maintenance is a cornerstone in developmental biology. Here, we present a mathematical model based on a branching process formalism that predicts average rates of proliferative and differentiative divisions in a given stem cell population. In the context of vertebrate neurogenesis, the model predicts complex non-monotonic variations in the rates of pp, pd and dd modes of division as well as in cell cycle length, in agreement with experimental results. Moreover, the model shows that the differentiation probability follows a binomial distribution, allowing us to develop equations to predict the rates of each mode of division. A phenomenological simulation of the developing spinal cord informed with the average cell cycle length and division rates predicted by the mathematical model reproduces the correct dynamics of proliferation and differentiation in terms of average numbers of progenitors and differentiated cells. Overall, the present mathematical framework represents a powerful tool to unveil the changes in the rate and mode of division of a given stem cell pool by simply quantifying numbers of cells at different times.

Synthetic approaches to study transcriptional networks and noise in mammalian systems

Synthetic biology aims to build new functional organisms and to rationally re-design existing ones by applying the engineering principle of modularity. Apart from building new life forms to perform technical applications, the approach of synthetic biology is useful to dissect complex biological phenomena into simple and easy to understand synthetic modules. Synthetic gene networks have been successfully implemented in prokaryotes and lower eukaryotes, with recent approaches moving ahead towards the mammalian environment. However, synthetic circuits in higher eukaryotes present a more challenging scenario, since its reliability is compromised because of the strong stochastic nature of transcription. Here, the authors review recent approaches that take advantage of the noisy response of synthetic regulatory circuits to learn key features of the complex machinery that orchestrates transcription in higher eukaryotes. Understanding the causes and consequences of biological noise will allow us to design more reliable mammalian synthetic circuits with revolutionary medical applications.

Smad2 and Smad3 cooperate and antagonize simultaneously in vertebrate neurogenesis

The transforming growth factor beta (TGF-β) pathway plays key roles in development and cancer. (TGF-β) signaling converges on the Smad2 and Smad3 effectors, which can either cooperate or antagonize to regulate their transcriptional targets. Here we performed in vivo and in silico experiments to study how such cooperativity and antagonism might function during neurogenesis. In vivo electroporation experiments in the chick embryo neural tube show that Smad2 and Smad3 cooperate to promote neurogenesis, as well as the transcription of Smad3 specific targets. Smad2 knockdown enhances neurogenesis and the transcription of Smad3 specific targets. A mathematical model of the TGF-β pathway fits the experimental results and predicts that the proportions of the three different trimeric complexes formed dictates the transcriptional responses of the R-Smads. As such, Smad2 targets are activated solely by the Smad2-Smad2-Smad4 complex, while Smad3 targets are activated both by Smad2-Smad3 Smad4 and Smad3- Smad3-Smad4 trimers. Since we have modeled the Smad responses onto arbitrary genes, we propose that this mechanism might be extended to additional activities of TGF-β in development and disease.

Interaction of chemical patterns in coupled layers

We investigate the interaction between reaction-diffusion systems coupled by diffusion. The photosensitive CDIMA (chorine dioxide-iodine-malonic acid) reaction allows us to study experimentally the mutual influence of two layers of Turing patterns coupled via a diffusive interaction. By illuminating each of the layers with different intensities of homogeneous external light, the chemical conditions in each layer can be shifted, allowing us to study the result of diffusive interaction between Turing patterns with different spatial configurations. Our experiments suggest a complex scenario for the interaction between different patterns, strongly dependent on the spatial characteristics of the interacting patterns. Numerical simulations are also reported in full agreement with experimental observations.

The role of asymmetric binding in ligand-receptor systems with 1:2 interaction ratio

Dynamical models for cellular ligand-receptor systems are among the most successful examples of mathematical approaches in systems biology. Here we present a general kinetic and mechanistic model for systems with asymmetric 1:2 ligand-receptor interaction ratio, such as erythropoietin and growth hormone systems. In these systems, the ligand presents two very different binding affinities to its receptor, and the weak interaction being often neglected for modeling purposes. Here, we demonstrate that the weak binding is the one tightly regulating the signaling, while the strong binding sets the threshold for the auto-inhibition effect characteristic of 1:2 asymmetric ligand-receptor systems. The model constitutes an improved mathematical framework for erythropoietin activation and equivalent biological processes, which are, due to their widespread use and relevance, on the forefront of pharmacological systems biology.

Selection of flow-distributed oscillation and Turing patterns by boundary forcing in a linearly growing, oscillating medium

We studied the response of a linearly growing domain of the oscillatory chemical chlorine dioxide-iodide-malonic acid (CDIMA) medium to periodic forcing at its growth boundary. The medium is Hopf-, as well as Turing-unstable and the system is convectively unstable. The results confirm numerical predictions that two distinct modes of pattern can be excited by controlling the driving frequency at the boundary, a flow-distributed-oscillation (FDO) mode of traveling waves at low values of the forcing frequency f , and a mode of stationary Turing patterns at high values of f . The wavelengths and phase velocities of the experimental patterns were compared quantitatively with results from dynamical simulations and with predictions from linear dispersion relations. The results for the FDO waves agreed well with these predictions, and obeyed the kinematic relations expected for phase waves with frequencies selected by the boundary driving frequency. Turing patterns were also generated within the predicted range of forcing frequencies, but these developed into two-dimensional structures which are not fully accounted for by the one-dimensional numerical and analytical models. The Turing patterns excited by boundary forcing persist when the forcing is removed, demonstrating the bistability of the unforced, constant size medium. Dynamical simulations at perturbation frequencies other than those of the experiments showed that in certain ranges of forcing frequency, FDO waves become unstable, breaking up into harmonic waves of different frequency and wavelength and phase velocity.

Fronts and pulses in an enzymatic reaction catalyzed by glucose oxidase

Waves and patterns in living systems are often driven by biochemical reactions with enzymes as catalysts and regulators. We present a reaction-diffusion system catalyzed by the enzyme glucose oxidase that exhibits traveling wave patterns in a spatially extended medium. Fronts and pulses propagate as a result of the coupling between the enzyme-catalyzed autocatalytic production and diffusion of hydrogen ions. A mathematical model qualitatively explains the experimental observations.

Designing an enzymatic oscillator: Bistability and feedback controlled oscillations with glucose oxidase in a continuous flow stirred tank reactor

The reaction of glucose with ferricyanide catalyzed by glucose oxidase from Aspergillus niger gives rise to a wide range of bistability as the flow rate is varied in a continuous flow stirred tank reactor. Oscillations in pH can be obtained by introducing a negative feedback on the autocatalytic production of H+ that drives the bistability. In our experiments, this feedback consists of an inflow of hydroxide ion at a rate that depends on [H+] in the reactor as k0[OH-]0[H+]/(K+[H+]). pH oscillations are found over a broad range of enzyme and ferricyanide concentrations, residence times (k0 (-1)), and feedback parameters. A simple mathematical model quantitatively accounts for the experimentally found oscillations.

On the orientation of stripes in fish skin patterning

This paper is focused on the study of the stripes orientation in the fish skin patterns. Based on microscopic observations of the pigment cells behavior at the embryonic stage, the key aspects of the pigmentation process are implemented in an experimental reaction-diffusion system. The experiment consists of a photosensitive Turing pattern of stripes growing directionally in one direction with controlled velocity. Different growth velocities of the system rearrange the stripes in the same three possible orientations observed in the skin of the colored fishes: parallel, oblique, and perpendicular. Our results suggest that the spreading velocity of the pigment cells in the fish dermis selects the orientation in the patterning processes.

Experimental evidence of localized oscillations in the photosensitive chlorine dioxide-iodine-malonic acid reaction

The interaction between Hopf and Turing modes has been the subject of active research in recent years. We present here experimental evidence of the existence of mixed Turing-Hopf modes in a two-dimensional system. Using the photosensitive chlorine dioxide-iodine-malonic acid reaction (CDIMA) and external constant background illumination as a control parameter, standing spots oscillating in amplitude and with hexagonal ordering were observed. Numerical simulations in the Lengyel-Epstein model for the CDIMA reaction confirmed the results.

Effect of axial growth on Turing pattern formation

We have performed one-dimensional and two-dimensional experiments and simulations to study the formation of patterns in a system that grows continuously in one direction. Depending on the growth velocity, three basic spatial configurations can be obtained: stripes that are parallel, oblique, or perpendicular to the growth direction. The dependence of the wavelength on the growth velocity has also been observed. Our results illustrate the importance of these growth mechanisms in determining the final configuration of chemical and biological pattern-forming processes.

Experimental steady pattern formation in reaction-diffusion-advection systems

We present here experimental evidence of a mechanism of a steady-chemical pattern formation called "flow-and-diffusion structures" (FDS). Experiments were performed using the photosensitive chlorine dioxide-iodine-malonic acid reaction, where the differential diffusion can be chemically controlled. Using the analogy between an advection boundary and a moving boundary, we obtain the formation of spatially periodic steady patterns, which matches all the previously theoretical predictions for FDS patterns. Numerical simulations are also reported in agreement with the experimental results.

Robustness and stability of flow-and-diffusion structures

Reaction-diffusion-advection systems have revealed an interesting variety of pattern formation mechanism during the last years. Inside this field, flow-and-diffusion structures (FDSs) appear as a generalization of the mechanism of spatial symmetry breaking for different diffusion coefficients and flow rates of activator and inhibitor. The recent experimental validation of FDSs situates these structures in the focus of the actual research. We will report here an experimental and numerical analysis of the theoretically predicted robustness of these flow-and-diffusion structures by using different boundary profiles of illumination used to obtain FDSs. The results here shown reveal important characteristics related with the coexistence and interaction between these structures.

Turing instability controlled by spatiotemporal imposed dynamics

The study of the spatiotemporal response of pattern forming systems to spatially resonant external forcing has unveiled striking new phenomena which challenge the understanding of self-organization in nonlinear, nonequilibrium systems. Here we show that a simple spatiotemporal two-dimensional forcing of a system supporting an intrinsic wavelength but no intrinsic frequency, under conditions of spatial resonance, may induce complex and entirely new spatiotemporal behaviors which do not reflect in any simple way the structure of the imposed forcing. We demonstrate this phenomenon in the Turing regime of the (photosensitive) CDIMA reaction by projecting a traveling stripe light pattern onto the reactor. By controlling the velocity of the forcing we induce distinct dynamical regimes that express the externally imposed frequency in new and intriguing ways. A detailed analysis of the experimental relevant parameters is presented.

Control of chemical pattern formation by a clock-and-wavefront type mechanism

The segmentation of many animals ranging from insects to mammals involves the sequential formation of stationary stripes of gene expression that are perpendicular to the growth axis of the developing embryo. This process has been accounted for by a variety of theoretical "clock-and-wavefront" type models that involve the arrest of an oscillation (the clock) at a moving boundary (the wavefront). Here, we demonstrate experimentally that progressive arrest of a homogeneous oscillation can control the symmetry as well as the wavelength of spatial structures in a chemical system. We show how a spontaneously formed, labyrinthine pattern can be converted into a pattern composed of ordered, parallel stripes and confirm a previously predicted proportionality between the wavelength and the period of the homogeneous oscillation. Our experiments provide the first experimental demonstration of a general mechanism for the control of pattern formation that has been hypothesized to operate in the context of biological morphogenesis.

Traveling-stripe forcing generates hexagonal patterns

We study the response of Turing stripe patterns to a simple spatiotemporal forcing. This forcing has the form of a traveling wave and is spatially resonant with the characteristic Turing wavelength. Experiments conducted with the photosensitive chlorine dioxide-iodine-malonic acid reaction reveal a striking symmetry-breaking phenomenon of the intrinsic striped patterns giving rise to hexagonal lattices for intermediate values of the forcing velocity. The phenomenon is understood in the framework of the corresponding amplitude equations, which unveils a complex scenario of dynamical behaviors.

Transverse instabilities in chemical Turing patterns of stripes

We present a theoretical and experimental study of the sideband instabilities in Turing patterns of stripes. We compare numerical computations of the Brusselator model with experiments in a chlorine dioxide-iodine-malonic acid (CDIMA) reaction in a thin gel layer reactor in contact with a continuously refreshed reservoir of reagents. Spontaneously evolving Turing structures in both systems typically exhibit many defects that break the symmetry of the pattern. Therefore, the study of sideband instabilities requires a method of forcing perfect, spatially periodic Turing patterns with the desired wave number. This is easily achieved in numerical simulations. In experiments, the photosensitivity of the CDIMA reaction permits control and modulation of Turing structures by periodic spatial illumination with a wave number outside the stability region. When a too big wave number is imposed on the pattern, the Eckhaus instability may arise, while for too small wave numbers an instability sets in forming zigzags. By means of the amplitude equation formalism we show that, close to the hexagon-stripe transitions, these sideband instabilities may be preceded by an amplitude instability that grows transient spots locally before reconnecting with stripes. This prediction is tested in both the reaction-diffusion model and the experiment.

Dynamics of Turing patterns under spatiotemporal forcing

We study, both theoretically and experimentally, the dynamical response of Turing patterns to a spatiotemporal forcing in the form of a traveling-wave modulation of a control parameter. We show that from strictly spatial resonance, it is possible to induce new, generic dynamical behaviors, including temporally modulated traveling waves and localized traveling solitonlike solutions. The latter make contact with the soliton solutions of Coullet [Phys. Rev. Lett. 56, 724 (1986)]] and generalize them. The stability diagram for the different propagating modes in the Lengyel-Epstein model is determined numerically. Direct observations of the predicted solutions in experiments carried out with light modulations in the photosensitive chlorine dioxide-iodine-malonic acid reaction are also reported.