D'Arcy Thompson was a true pioneer, applying mathematical concepts and analyses to the question of morphogenesis over 100 years ago. The centenary of his famous book,
, is therefore a great occasion ...on which to review the types of computer modeling now being pursued to understand the development of organs and organisms. Here, I present some of the latest modeling projects in the field, covering a wide range of developmental biology concepts, from molecular patterning to tissue morphogenesis. Rather than classifying them according to scientific question, or scale of problem, I focus instead on the different ways that modeling contributes to the scientific process and discuss the likely future of modeling in developmental biology.
The interpretation of morphogen gradients is a pivotal concept in developmental biology, and several mechanisms have been proposed to explain how gene regulatory networks (GRNs) achieve ...concentration‐dependent responses. However, the number of different mechanisms that may exist for cells to interpret morphogens, and the importance of design features such as feedback or local cell–cell communication, is unclear. A complete understanding of such systems will require going beyond a case‐by‐case analysis of real morphogen interpretation mechanisms and mapping out a complete GRN ‘design space.’ Here, we generate a first atlas of design space for GRNs capable of patterning a homogeneous field of cells into discrete gene expression domains by interpreting a fixed morphogen gradient. We uncover multiple very distinct mechanisms distributed discretely across the atlas, thereby expanding the repertoire of morphogen interpretation network motifs. Analyzing this diverse collection of mechanisms also allows us to predict that local cell–cell communication will rarely be responsible for the basic dose‐dependent response of morphogen interpretation networks.
Synopsis
Understanding how gene regulatory networks (GRNs) achieve particular biological functions is a central question in systems biology. Systems biology promises to go beyond a case‐by‐case understanding of individual networks to map out the complete design space of mechanistic possibilities that underlie biological functions. Can such maps serve as useful theoretical frameworks in which to explore the general design principles for these functions? Towards addressing these questions, we created the first design space for a morphogen interpretation function.
In order to generate a design space for such a function, we enumerated all possible wiring designs of GRNs consisting of three genes and tested their ability to perform one particular morphogen interpretation function; stripe formation, as it represents a simplified form of the much studied French flag problem and is a commonly found gene expression pattern (Figure 1A). We found that only 5% of GRNs had the ability to generate a single stripe of gene expression when simulated with a fixed morphogen input in a one‐dimensional model.
We hypothesized that the core mechanisms for producing the stripe of gene expression should be represented by topologies that contain only the necessary and sufficient gene–gene interactions for that function. Hence, we utilized the notions of complexity and neighborhood to generate a complexity atlas. GRNs of such an atlas (represented by nodes) are considered neighbors if they differ by a single gene–gene interaction (neighboring GRN nodes are connected by edges). Such a metagraph (graph of graphs) can then be reorganized using complexity (number of gene–gene interactions) to determine a GRNs position in the y axis, whereas GRNs are spaced in the x axis with the aim of reducing edge crossing (Figure 5A). This reorganization reveals a striking structure, where ‘stalactites’ of complexity can be seen protruding from the bottom of the atlas. Each of these stalactites converges on a single ‘core’ topology that by extensive analysis we find represents a distinct mechanism.
The mechanisms employ a diverse range of distinct space–time behaviors, and the underlying core topologies display design features such as modularity and feed‐forward. We mapped the mechanisms to the complexity atlas by analyzing how each particular GRN of the atlas was working. The GRNs functioning via the different mechanisms are highlighted by the different colors in Figure 5A. Mechanisms thus occupy large regions of separated topology space, suggesting them to be discrete. Analyzing transitions between mechanisms through parameter space confirms this to be the case.
We find that three of the mechanisms are employed in real patterning systems, including both blastoderm patterning in Drosophila and mesoderm specification in Xenopus (Figure 5B). The remaining three mechanisms are thus candidates for employment in other patterning systems. We explored the performance features of these mechanisms, which suggest that some have features such as robustness to parameter variation that make them highly likely to be employed in particular patterning contexts.
Only one of the six‐core mechanisms absolutely requires cell–cell communication for functionality, prompting us to predict that cell–cell communication will rarely be responsible for the basic dose response of morphogen interpretation networks. However, we show how cell–cell communication has an important role in robust stripe generation in the face of a noisy morphogen input and in fine tuning the quantitative details of stripe patterning.
In summary, the complexity atlas approach is an amendable approach to any system with a clear genotype–function relationship. We demonstrate how certain functions such as morphogen interpretation may have a range of potential solutions in contrast to previous studies that analyzed more constrained functions. Furthermore, we demonstrate how such an approach can be utilized to define a ‘design space’ for a given biological function that describes the different mechanistic possibilities and how they relate to one another (Figure 5). Such a design space can be used practically as a guide to discern which patterning mechanisms are likely be at work in a particular context throwing up less intuitive possibilities with powerful performance features.
Although >450 different topologies can achieve the same multicellular patterning function, they can be grouped into six main classes, which operate using different underlying dynamics.
Alternative designs for the same functions can therefore split into two types: (a) topology alterations that retain the same underlying dynamics and (b) alterations that utilize a completely different underlying dynamical mechanism.
This segregation of networks into distinct dynamical mechanisms can be revealed by the shape of the topology atlas itself.
Cell–cell communication is not usually part of the causal mechanism underlying a band‐pass response during morphogen interpretation, but it can tune the result or increase robustness.
One of the most fundamental questions in biology is that of biological pattern: how do the structures and shapes of organisms arise? Undoubtedly, the two most influential ideas in this area are those ...of Alan Turing's 'reaction-diffusion' and Lewis Wolpert's 'positional information'. Much has been written about these two concepts but some confusion still remains, in particular about the relationship between them. Here, we address this relationship and propose a scheme of three distinct ways in which these two ideas work together to shape biological form.
A major challenge in systems biology is to understand the relationship between a circuit's structure and its function, but how is this relationship affected if the circuit must perform multiple ...distinct functions within the same organism? In particular, to what extent do multi‐functional circuits contain modules which reflect the different functions? Here, we computationally survey a range of bi‐functional circuits which show no simple structural modularity: They can switch between two qualitatively distinct functions, while both functions depend on all genes of the circuit. Our analysis reveals two distinct classes: hybrid circuits which overlay two simpler mono‐functional sub‐circuits within their circuitry, and emergent circuits, which do not. In this second class, the bi‐functionality emerges from more complex designs which are not fully decomposable into distinct modules and are consequently less intuitive to predict or understand. These non‐intuitive emergent circuits are just as robust as their hybrid counterparts, and we therefore suggest that the common bias toward studying modular systems may hinder our understanding of real biological circuits.
Synopsis
A computational survey of simple bi‐functional gene circuits reveals a spectrum of possible modularity. While many circuits are decomposable into sub‐modules, others are not. These non‐modular, non‐intuitive circuits may be just as common in nature.
A wide range of simple wiring designs is computationally screened to find circuits capable of two distinct patterning functions: lateral inhibition and lateral induction.
While some of these bi‐functional circuits contain clear function‐specific sub‐modules (hybrids), many other circuits do not (emergent).
The distinction between hybrid circuits and emergent circuits can be seen in their dynamics, as well as their structure.
Although emergent circuits are less intuitive and harder to understand than modular ones, they are just as robust, and thus equally biologically plausible.
A computational survey of simple bi‐functional gene circuits reveals a spectrum of possible modularity. While many circuits are decomposable into sub‐modules, others are not. These non‐modular, non‐intuitive circuits may be just as common in nature.
During embryonic development, epithelial cell blocks called somites are periodically formed according to the segmentation clock, becoming the foundation for the segmental pattern of the vertebral ...column. The process of somitogenesis has recently been recapitulated with murine and human pluripotent stem cells. However, an in vitro model for human somitogenesis coupled with the segmentation clock and epithelialization is still missing. Here, we report the generation of human somitoids, organoids that periodically form pairs of epithelial somite-like structures. Somitoids display clear oscillations of the segmentation clock that coincide with the segmentation of the presomitic mesoderm. The resulting somites show anterior-posterior and apical-basal polarities. Matrigel is essential for epithelialization but dispensable for the differentiation into somite cells. The size of somites is rather constant, irrespective of the initial cell number. The amount of WNT signaling instructs the proportion of mesodermal lineages in somitoids. Somitoids provide a novel platform to study human somitogenesis.
Turing’s theory of pattern formation is a universal model for self-organization, applicable to many systems in physics, chemistry, and biology. Essential properties of a Turing system, such as the ...conditions for the existence of patterns and the mechanisms of pattern selection, are well understood in small networks. However, a general set of rules explaining how network topology determines fundamental system properties and constraints has not been found. Here we provide a first general theory of Turing network topology, which proves why three key features of a Turing system are directly determined by the topology: the type of restrictions that apply to the diffusion rates, the robustness of the system, and the phase relations of the molecular species.
During somitogenesis in embryos, a posteriorly moving differentiation front arrests the oscillations of “segmentation clock” genes, leaving behind a frozen, periodic pattern of expression stripes. ...Both mathematical theories and experimental observations have invoked a “clock and wavefront” model to explain this phenomenon, in which long-range molecular gradients control the movement of the front and therefore the placement of the stripes in the embryo. Here, we develop a fundamentally different model—a progressive oscillatory reaction-diffusion (PORD) system driven by short-range interactions. In this model, posterior movement of the front is a local, emergent phenomenon that, in contrast to the clock and wavefront model, is not controlled by global positional information. The PORD model explains important features of somitogenesis, such as size regulation, that previous reaction-diffusion models could not explain. Moreover, the PORD and clock and wavefront models make different predictions about the results of FGF-inhibition and tissue-cutting experiments, and we demonstrate that the results of these experiments favor the PORD model.
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•A systematic computational screen identifies networks based on behavior•Computation shows that somitogenesis can be explained by short-range interactions•Short-range and long-range models are tested head-to-head in silico and in vivo•Short-range models explain aspects of somitogenesis that previous models cannot
Using a systematic computational approach and in vivo experiments, Cotterell et al. challenge a 40-year-old model that explains large-scale embryonic patterns in terms of long-range gradients. Instead, they show that these patterns can arise from short-range interactions and that a modified reaction-diffusion mechanism can drive the self-organization observed during somitogenesis.
A Turing mechanism implemented by BMP, SOX9 and WNT has been proposed to control mouse digit patterning. However, its generality and contribution to the morphological diversity of fins and limbs has ...not been explored. Here we provide evidence that the skeletal patterning of the catshark Scyliorhinus canicula pectoral fin is likely driven by a deeply conserved Bmp-Sox9-Wnt Turing network. In catshark fins, the distal nodular elements arise from a periodic spot pattern of Sox9 expression, in contrast to the stripe pattern in mouse digit patterning. However, our computer model shows that the Bmp-Sox9-Wnt network with altered spatial modulation can explain the Sox9 expression in catshark fins. Finally, experimental perturbation of Bmp or Wnt signalling in catshark embryos produces skeletal alterations which match in silico predictions. Together, our results suggest that the broad morphological diversity of the distal fin and limb elements arose from the spatial re-organization of a deeply conserved Turing mechanism.
Dynamics of gene circuits shapes evolvability Jiménez, Alba; Munteanu, Andreea; Sharpe, James
Proceedings of the National Academy of Sciences - PNAS,
02/2015, Letnik:
112, Številka:
7
Journal Article
Recenzirano
Odprti dostop
Significance It is widely accepted that the structure of a biological system limits the range of possible novel phenotypes accessible by mutation. Here we show that it is not only the phenotype that ...determines this evolvability, but also the dynamics of how that phenotype is built during development. We perform theoretical analysis on a group of simple gene regulatory circuits that have recently been shown to fall into a handful of distinct dynamical mechanisms all producing the same phenotype: interpreting a morphogen gradient into a single-domain of gene expression. We find that the dynamical mechanisms underlying each circuit impose strong constraints on its evolvability, as hypothesized in a more general context by John Maynard Smith in the 1980s.
To what extent does the dynamical mechanism producing a specific biological phenotype bias the ability to evolve into novel phenotypes? We use the interpretation of a morphogen gradient into a single stripe of gene expression as a model phenotype. Although there are thousands of three-gene circuit topologies that can robustly develop a stripe of gene expression, the vast majority of these circuits use one of just six fundamentally different dynamical mechanisms. Here we explore the potential for gene circuits that use each of these six mechanisms to evolve novel phenotypes such as multiple stripes, inverted stripes, and gradients of gene expression. Through a comprehensive and systematic analysis, we find that circuits that use alternative mechanisms differ in the likelihood of reaching novel phenotypes through mutation. We characterize the phenotypic transitions and identify key ingredients of the evolutionary potential, such as sensitive interactions and phenotypic hubs. Finally, we provide an intuitive understanding on how the modular design of a particular mechanism favors the access to novel phenotypes. Our work illustrates how the dynamical mechanism by which an organism develops constrains how it can evolve. It is striking that these dynamical mechanisms and their impact on evolvability can be observed even for such an apparently simple patterning task, performed by just three-node circuits.
To determine the effect of taping the top of face masks on air particle counts directed toward the eye during simulated intravitreal injections.
Prospective observational crossover study.
Thirteen ...healthy subjects were recruited. Each wore a cloth, surgical, or N95 mask in randomized order. The number of air particles were quantified by using a particle counter suspended over the right eye while each subject breathed normally, deeply, or spoke using a standardized script. Particle counts were obtained with the top of each mask taped and not taped. The main outcome measurements were particle counts of 0.3, 0.5, 1, 3, 5, and 10 μm and total particle counts.
Taping cloth masks while subjects were speaking significantly reduced particle counts for the 0.3- (P = .03), 0.5- (P = .01), and 1-μm (P = .03) particles and total particle counts (P = .008) compared to no taping. Taping the top of cloth masks during normal or deep breathing did not significantly affect particle counts compared to no taping. Taping the top of surgical or N95 masks did not significantly alter particle counts for any breathing condition tested.
Taping the top of cloth masks prior to simulated intravitreal injections significantly reduced air particle counts directed toward the eye when subjects were speaking compared to no taping. This may have implications for decreasing air particles reaching the eye during intravitreal injections, including aerosolized droplets from a patient's mouth that may carry oral pathogens.
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