Table of Contents
Overview
Definition and Importance
Pattern formation is a fundamental biological process that describes how cells in a developing organism organize themselves into complex structures and functions over time and space. This phenomenon is particularly evident during embryogenesis, where initially equivalent cells differentiate into various cell types, leading to the formation of distinct tissues and organs. For instance, in the fruit fly Drosophila, coordinated control of cell fates is crucial for proper development, illustrating the intricate mechanisms underlying pattern formation.[6.1] The mechanisms of pattern formation are genetically controlled and often involve cells sensing their position within a morphogen gradient. This sensing is complemented by short-distance cell-to-cell communication through signaling pathways, which helps refine the initial patterns established by the morphogen gradients.[6.1] The conceptual framework for understanding these processes was notably advanced by the French flag model in the 1960s, which illustrates how positional information can dictate cell fate decisions.[6.1] In addition to developmental biology, pattern formation is observed in various prokaryotic systems, where patterns can be transient, such as those formed by swimming bacteria in response to chemoattractants, or more stable, as seen in the one-dimensional arrangements of cells in cyanobacteria and the complex three-dimensional structures in bacterial fruiting bodies.[1.1] Understanding these patterns is essential for comprehending broader biological phenomena, including evolutionary developmental biology, where changes in the timing and positioning of developmental events can lead to significant morphological diversity among organisms.[6.1]Mechanisms of Pattern Formation
Pattern formation in biological systems is a complex process that involves various mechanisms, including morphogen gradients, gene interactions, and mathematical modeling. One of the foundational concepts in understanding these mechanisms is the role of morphogen gradients, which subdivide a naive cell field into distinct zones of gene expression. For instance, in Drosophila embryonic development, the dorsal gradient interacts with embryo morphology and the Toll signaling pathway, influencing the expression of key regulatory genes such as twist and snail, which act as positive and negative regulators during mesoderm development.[7.1] The French flag model proposed by Lewis Wolpert illustrates how morphogen gradients can activate the expression of different genes at varying concentrations. In this model, a graded signal activates the expression of "blue," "white," and "red" genes at high, intermediate, and low concentrations, respectively.[8.1] This concept is further supported by the observation that repressive interactions between morphogen-regulated genes are crucial for interpreting these gradients. A notable example is the cross-repression that contributes to the partitioning of the Drosophila neuroectoderm into three distinct columns along the dorsal-ventral (DV) axis.[9.1] In Drosophila, early developmental stages rely heavily on graded distributions of transcription factors. The anterior-to-posterior gradient of Bicoid (Bcd), a transcriptional activator, is essential for specifying anterior body segments, while the ventral-to-dorsal gradient of Dorsal (Dl) organizes the embryo by both activating and repressing gene expression.[10.1] This interplay of morphogen gradients and gene regulation exemplifies the intricate mechanisms of pattern formation, where initially equivalent cells in a developing tissue respond to their positional information along these gradients, followed by localized cell-to-cell communication to refine the emerging patterns.[11.1] Mathematical models, such as Turing's reaction-diffusion theory, provide a theoretical framework for understanding biological pattern formation. Turing's model explains how natural patterns, such as stripes and spots, can arise from a homogeneous state through the interaction of chemical substances.[17.1] His work has had a profound impact on developmental biology, offering insights into how cells differentiate and change shape in response to morphogen gradients.[16.1] The Swift-Hohenberg equation, another mathematical model, has also been applied to study complex pattern formation in biological tissues, demonstrating its relevance across various fields, including biology and ecology.[19.1]In this section:
History
Early Theories
Early theories regarding pattern formation in organisms have often centered on the role of genetic mutations and their contributions to evolutionary processes. Genetic mutations are a fundamental aspect of biological diversity, frequently resulting in unique coat patterns and colors in animals. For instance, the "Merle" gene is a notable example that produces distinctive coat patterns characterized by patches of diluted pigment. However, this mutation can also lead to adverse health effects, such as hearing loss or vision problems when present in double doses, highlighting the dual nature of genetic mutations in influencing both aesthetic traits and health outcomes.[52.1] In the broader context of evolution, the rich diversity of animal fur colors and patterns is primarily attributed to naturally occurring mutations that have been favored through natural selection. These mutations not only enhance the visual appeal of various species but also play a crucial role in their survival and adaptation to different environments.[53.1] For example, variations in skin coloration and patterns have enabled certain species to effectively blend into their surroundings or mimic other species, which can deter predators or assist in ambushing prey. This illustrates how genetic changes can lead to evolutionary strategies that enhance survival.[54.1]Turing's Contribution
Alan Turing's 1952 article, "The Chemical Basis of Morphogenesis," represents a groundbreaking contribution to the understanding of spatial pattern formation in biological systems. In this seminal work, Turing was the first to propose a mathematical model that demonstrated how spatial patterns could emerge from the instability of a reaction-diffusion mechanism involving two chemicals—one acting as an activator and the other as an inhibitor.[64.1] This model challenged the reductionist perspective that biological structures arise solely from deterministic processes, suggesting instead that complex patterns could emerge from non-patterning processes.[65.1] Turing's work not only provided a theoretical framework for understanding biological patterning but also included the first computer simulations of such phenomena, marking a significant advancement in the field of developmental biology.[51.1] His insights opened new avenues for research, allowing scientists to explore the chemical reactions and mechanical forces that enable embryos to self-organize from a single cell. Alan Turing's 1952 paper on the origin of biological patterning introduced a mathematical framework that revolutionized the understanding of pattern formation in biological systems. His model not only provided a theoretical basis for simulating and predicting these patterns but also included the first computational simulations of pattern formation, which marked a significant advancement in the field of developmental biology.[51.1] Turing's insights opened new avenues for exploring how organisms develop and maintain structural diversity, integrating reaction-diffusion theories with genetic data to enhance predictions about pattern emergence.[66.1] This framework has been foundational in understanding complex biological processes, allowing scientists to incorporate factors such as environmental influences and genetic regulation into their models.[62.1] Turing's work has thus laid the groundwork for future research in both biology and mathematics, offering a deeper understanding of the mechanisms underlying pattern formation.[62.1] Alan Turing's groundbreaking work in his 1952 paper, "The Chemical Basis of Morphogenesis," introduced a mathematical model that fundamentally transformed the understanding of spatial pattern formation in biological systems. He proposed that these patterns could emerge from the instability of a reaction-diffusion mechanism involving two chemicals, one acting as an activator and the other as an inhibitor.[64.1] This innovative framework not only addressed a previously insurmountable intellectual challenge in developmental biology but also opened new avenues for research, allowing scientists to directly engage with the chemical reactions and mechanical forces that enable embryos to self-organize from a single cell.[51.1] Turing's reaction-diffusion model has since become a foundational concept in mathematical biology, serving as a powerful paradigm for self-organization and being increasingly applied to real experimental systems.[66.1] The implications of Turing's work extend to understanding complex biological processes, offering insights into how organisms develop and maintain structural diversity, and facilitating better predictions and manipulations of patterns in various biological contexts.[66.1]Recent Advancements
Reaction-Diffusion Theories
Reaction-diffusion theories, introduced by Alan Turing in 1952, serve as a foundational framework for understanding the emergence of spatial patterns in biological systems. Turing patterns, which are stable spatial patterns resulting from the interplay of chemical reactions and molecular diffusion, underlie many developmental processes in organisms.[127.1] These patterns are crucial for comprehending complex biological phenomena, including organ development and structural diversity.[126.1] Turing's work has opened new avenues in developmental biology, allowing researchers to explore how organisms self-organize from a single cell through chemical reactions and mechanical forces.[90.1] Despite the theoretical advancements, implementing biological systems that generate Turing patterns remains a significant challenge, as evidenced by ongoing efforts to engineer synthetic genetic networks capable of producing these patterns.[126.1] Overall, Turing patterns manifest across various biological contexts, providing valuable insights into the mechanisms of pattern formation and the self-organization of biological structures.[125.1] Recent advancements in the application of reaction-diffusion models have enabled researchers to better predict and manipulate pattern formation in biological contexts. By integrating these models with genetic data, scientists can explore the mechanisms underlying the emergence of patterns and their implications for developmental biology.[125.1] However, challenges remain in implementing these models in real-world scenarios, particularly regarding the robustness and reproducibility of generated patterns in the face of perturbations.[128.1] Moreover, the exploration of Turing patterns has expanded into synthetic biology, where researchers have engineered living cellular systems capable of generating Turing patterns through synthetic genetic networks.[126.1] This innovative approach not only enhances our understanding of pattern formation but also opens avenues for potential applications in conservation biology and other fields.[125.1] Overall, reaction-diffusion theories continue to be a vibrant area of research, driving forward our comprehension of the complex interplay between biological processes and pattern formation.Computational Modeling
Recent advancements in computational modeling have significantly enhanced the understanding and simulation of complex pattern formation processes across various scientific domains. Notably, the integration of physics-informed machine learning and operator learning has emerged as promising approaches to reduce the computational costs associated with simulating real patterns, leveraging large image datasets to improve efficiency and accuracy in modeling.[101.1] The study of localized patterns has also benefited from innovative mathematical tools and numerical techniques, which have been bolstered by advancements in computational power. These developments have facilitated the identification of new localized patterns and provided deeper insights into their formation mechanisms.[102.1] Furthermore, comprehensive reviews highlight the role of artificial intelligence in optimizing simulations and modeling complex systems in fields such as materials engineering and energy systems, confirming the potential of AI algorithms to enhance the modeling landscape.[103.1] In biological contexts, computational models have been pivotal in elucidating the interactions that govern pattern formation during processes such as cell aggregation and bone formation. For instance, models have provided crucial insights into the morphodynamic processes underlying limb skeletal patterning, illustrating the intricate relationships between biological components.[104.1] Moreover, the application of computational modeling in tissue engineering has led to the development of advanced techniques such as 3D bioprinting. This technology allows for the precise layering of biological materials to create complex tissue constructs, addressing the challenges of replicating the complexity of natural tissues.[122.1] The design of computational models serves as a guide in bioprinting and biomanufacturing, facilitating the creation of functional tissue structures.[107.1] Additionally, the advent of organoids—3D tissue culture systems that mimic the architecture and function of native organs—demonstrates the potential of computational modeling in programming biological patterns. These systems enable the testing of synthetic genetic programs that govern cell communication and tissue patterning.[121.1]In this section:
Organ DevelopmentSynthetic BiologyConservation BiologyMachine LearningArtificial Intelligence
Biological Implications
Developmental Biology
In developmental biology, pattern formation refers to the generation of complex organizations of cell fates in space and time. This process describes how initially equivalent cells in a developing tissue, such as an embryo, can assume distinct forms and functions. Embryogenesis, exemplified by organisms like the fruit fly Drosophila, involves the coordinated control of cell fates. Pattern formation is genetically regulated and typically requires each cell to sense and respond to its position along a morphogen gradient. This is often followed by short-distance cell-to-cell communication through signaling pathways, which helps to refine the initial pattern. The conceptual framework for understanding this process was first articulated in the 1960s through the French flag model, which illustrates how gradients of diffusible substances (morphogens) specify the differentiative pathways that cells should follow.[129.1] More broadly, the morphology of organisms is influenced by the mechanisms of evolutionary developmental biology, which involve changes in the timing and positioning of specific developmental events in the embryo.[129.1] Pattern formation occurs in several stages, particularly in secondary fields such as developing limbs. These stages include defining the cell field, establishing specific signaling centers to provide positional information, recording this information on a cell-by-cell basis, and finally, differentiating cells in response to additional cues based on the encoded positional information. Various models, including gradient models, reaction-diffusion models, and induction models, have been proposed to explain these processes.[131.1] The study of pattern formation mechanisms is not only vital for understanding embryonic development but also sheds light on evolutionary processes. Research indicates that early animal evolution may have relied on subcellular patterning mechanisms alongside newly evolved cell-cell communication pathways. This suggests that insights into the mechanisms of pattern formation and complexity in single cells could be crucial for understanding the evolutionary trajectories of both plants and animals.[132.1] Model organisms, such as Hydra, have been instrumental in elucidating the basic mechanisms underlying biological pattern formation. Hydra's radially symmetric structure provides key insights into the establishment of secondary axes and the evolution of bilateral body plans in higher animals.[133.1] Furthermore, genetic variation plays a significant role in the evolution of pattern formation mechanisms across different species. Genetic diversity within populations introduces variability that can influence developmental processes, thereby affecting how organisms adapt and evolve over time.[136.1] Systematic genetic analyses of mutations in Drosophila have provided a detailed understanding of the processes controlling development, particularly in relation to pattern formation during embryogenesis. These studies have established definitive proof of the involvement of specific genetic mutations in disrupting signaling pathways essential for proper development.[142.1] Notably, the Toll pathway has been identified as a central component in regulating dorsoventral polarity in the Drosophila embryo, highlighting its critical role in the overall patterning process.[144.1] Furthermore, insights gained from these genetic analyses have implications for understanding neurodevelopmental disorders in humans, as mutations in numerous genes are known to cause such disorders, often resulting in abnormal motor behavior and cognitive deficits.[145.1]Morphogen Gradients
Morphogen gradients are critical for the organized spatial distribution of cells during embryonic development and can also play a role in tissue maintenance and regeneration in mature organisms. These gradients are typically formed by secreted proteins that diffuse from a localized source, creating a concentration gradient across a field of cells. Morphogens can include cytoplasmic proteins, such as transcription factors, or secreted signaling molecules that travel between cells. A common mechanism for gradient formation involves the localized transcription of a gene encoding a secreted protein, followed by the movement of the signaling molecule across or through a field of cells.[158.1] The response of cells to morphogen gradients is highly dependent on their position within the gradient. Cells located at different distances from the source of the morphogen will experience varying concentrations, leading to distinct differentiation pathways and cell types.[139.1] For example, the fibroblast growth factor 8 (FGF8) plays a significant role during vertebrate axis elongation, where its mRNA is transcribed at the posterior tip of the embryo, contributing to the spatial organization of developing tissues.[141.1] Moreover, the concept of morphogen gradients has been instrumental in understanding how cells interpret and respond to varying signal levels, which can lead to region-specific transcriptional responses and ultimately determine cell fate.[161.1] The establishment of these gradients can occur through mechanisms such as diffusion and decay, as well as through more complex processes like planar transcytosis, where morphogens are actively moved between cells via cycles of exocytosis and endocytosis.[162.1] Despite the established framework of morphogen gradients, several mechanistic questions remain, particularly regarding how these signals are perceived and interpreted by cells. Disruptions in morphogen signaling pathways can lead to developmental abnormalities, highlighting the importance of precise gradient formation and maintenance in normal biological processes.[163.1] Thus, understanding morphogen gradients is essential for elucidating the mechanisms of pattern formation in biological systems.In this section:
Mathematical Framework
Turing Patterns
The concept of Turing patterns, introduced by Alan Turing, describes the emergence of spatial instability and pattern formation in reaction-diffusion systems. Since Turing's initial description, the Turing instability has become a widely recognized mechanism for investigating pattern formation across various biological, chemical, and physical systems.[191.1] This theoretical framework begins with Turing's reaction-diffusion equations, which illustrate how patterns can emerge from a homogeneous system and the mechanisms that govern their development.[177.1] Experimental evidence indicates that environmental factors, such as temperature differences, can significantly influence the dynamics of pattern formation, highlighting the importance of these factors in mathematical models of biological pattern formation.[191.1] Alan Turing's 1952 paper on the origin of biological patterning addressed a significant intellectual challenge that had previously led the developmental biologist Hans Driesch to abandon his scientific pursuits in favor of philosophy.[185.1] Turing developed a theory to explain how certain patterns in nature could spontaneously arise from simple chemical systems, marking a notable departure from his earlier focus on computation.[186.1] His work not only provided an analytical proof but also included the first computer simulations of pattern formation influenced by stochastic fluctuations, representing a pioneering instance of computational experimentation in biology.[185.1] This innovative approach opened new perspectives in developmental biology, emphasizing the chemical reactions and mechanical forces that enable embryos to self-organize from a single cell.[185.1] Turing's insights, alongside those of D'Arcy Wentworth Thompson, who argued that biological shapes could be understood through geometric principles rather than mere randomness, have profoundly influenced contemporary views on the relationship between mathematics and the natural sciences.[188.1] Thompson's seminal work, "On Growth and Form," challenged both mathematicians and naturalists to consider biological shapes as geometric forms describable by principles of physics and mathematics, rather than as chaotic and random configurations.[188.1] Turing patterns play a significant role in developmental biology, particularly in understanding how environmental factors, such as temperature, quantitatively influence pattern formation. Mathematical models have become essential in simulating various patterns observed in biological forms, as they help elucidate how temperature affects the diffusion rates of morphogens—substances that influence tissue patterning—thereby altering basic patterns to some extent.[190.1] The concept of morphogens, which are diffusible molecules that affect the internal state of developing tissues in a concentration-dependent manner, was introduced by Alan Turing.[192.1] In the context of specific organisms, such as yeast, patterns emerge from genetic mechanisms that control adhesion, differentiation, and spatial organization, optimizing resource use and environmental adaptation.[193.1] Genes like FLO11 in Saccharomyces cerevisiae are crucial for structured colony formation, as they promote cell-cell interactions and surface attachment, highlighting the interplay between genetic factors and environmental influences in pattern formation.[193.1]Applications in Biology
Mathematical models, particularly reaction-diffusion equations, play a crucial role in understanding biological pattern formation. These equations arise in systems with multiple interacting components, such as chemical reactions, and are instrumental in describing phenomena like the spatial distribution of species in biological contexts.[194.1] For instance, coupled reaction-diffusion equations can model the interactions between messenger RNA and various non-coding microRNAs within biological cells, illustrating how different species influence one another.[195.1] Additionally, these models can be interpreted in the context of predator-prey dynamics, where the spatial diffusion of species is combined with their interactions, as seen in studies of liver infections.[196.1] One of the classical frameworks for explaining biological patterns is the Turing model, which incorporates long-range inhibition and short-range activation to generate diverse periodic patterns, such as spots and stripes. This model has been applied to various biological contexts, including the formation of animal coat markings.[198.1] The integration of computational analysis with genetic experiments has further enhanced our understanding of pattern formation, allowing researchers to predict patterning defects in mutants and identify regulatory links within complex mechanisms.[199.1] Moreover, mathematical models have been pivotal in elucidating the dynamics of biological pattern formation. For example, the Gray-Scott model, which addresses autocatalysis in chemical reactions, serves as a valuable tool for studying bistability in pattern formation.[203.1] In limb development, mathematical modeling has been employed to explore chondrogenic pattern formation, distinguishing between models that focus on limb bud growth and those that examine pre-skeletal cartilage patterning.[204.1] The interplay between mathematical abstraction and empirical observation has led to significant breakthroughs in our understanding of biological systems. For instance, the concept of morphogens, which are diffusible molecules affecting cellular behavior, was introduced by Alan Turing and has become fundamental in developmental biology.[205.1] Recent advancements have further solidified the role of mathematical models in validating experimental hypotheses, demonstrating their importance in the study of developmental processes.[206.1]Case Studies
Examples in Nature
A notable instance of natural pattern formation is the Turing pattern, introduced by Alan Turing in 1952. His theory of reaction-diffusion systems explains how uniform systems can evolve into organized patterns like spots and stripes through chemical reactions and diffusion processes.[231.1] These patterns are not merely theoretical; they are observed in biological contexts, offering insights into developmental pattern formation mechanisms.[231.1] In embryogenesis, pattern formation is vital for developing specific structures. For example, limb development involves defining the cell field, establishing signaling centers, recording positional information, and differentiating cells accordingly.[217.1] This sequence is crucial for forming limbs and other structures, showcasing the complexity of biological patterning. Research into mammalian development has uncovered significant insights into genetic and epigenetic processes governing embryogenesis. Epigenetic maps of early human embryogenesis have enhanced our understanding of genetic regulation's interaction with environmental factors in shaping developmental patterns.[219.1] The specification of primordial germ cells (PGCs) during early embryogenesis is critical for genetic information transmission, with defects potentially leading to infertility or birth defects.[220.1] The study of pattern formation also underscores the importance of nonlinear dynamics in understanding biological self-organization. Nonlinear dynamics involves complex systems where simple rules lead to emergent behaviors, such as spontaneous pattern formation and collective behaviors in biological entities.[224.1] This approach helps decipher the intricate interactions that result in organized structures in living organisms, highlighting the significance of pattern formation in biology.In this section:
Challenges And Future Directions
Robustness Problem
The robustness problem in pattern formation research pertains to the challenge of ensuring that generated patterns remain consistent and reproducible despite various perturbations. This issue is particularly complex due to the inherent biological heterogeneity and the multitude of factors that can influence pattern formation, such as domain conditions, reaction time scales, and boundary conditions. For instance, gene-expression time delays can be integrated into Turing models, which are used to describe pattern formation dynamics, allowing for the exploration of how these delays affect the timing of pattern onset in response to fluctuations in initial conditions.[268.1] The robustness of biological patterns is crucial for the reliable generation of complex structures in higher organisms. This reproducibility is achieved through models of biological pattern formation, which are represented by nonlinear partial differential equations that describe the production and decay rates, as well as the diffusion of substances involved in pattern formation.[264.1] The development of an organism, such as a human, involves numerous interacting components and complex processes, including signal transduction, gene expression, pattern formation, transport of material, growth, and mechanical forces.[266.1] In this context, mathematical models and analyses play a significant role in understanding development, particularly through the concept of the morphogenetic landscape, which refers to the spatial distribution of extracellular state variables to which cells in developing tissues respond.[266.1] These models enhance our understanding of the underlying biological mechanisms by providing insights into how diffusible molecules, known as morphogens, affect the internal state of cells in a concentration-dependent manner.[266.1]Integration with Genetic Data
Synthetic biology plays a crucial role in enhancing our understanding of pattern formation by providing a complementary approach to traditional biological studies. This field allows researchers to create simpler and more controllable systems that can elucidate the mechanisms underlying biological pattern formation, which is often obscured by the complexities of natural systems.[276.1] By engineering microbial populations and communities, synthetic biology enables the generation of sophisticated spatial patterns, thereby facilitating the exploration of general principles of pattern formation.[278.1] Recent advancements in synthetic biology have led to innovative applications, such as using periodic stripe pattern formation as a model to deepen our understanding of biological patterns and to promote applications in areas like tissue engineering.[279.1] This bottom-up approach not only aids in the investigation of fundamental biological processes but also holds promise for practical applications in various fields, including medicine and environmental science.[298.1] The integration of synthetic biology with genetic data is pivotal in understanding pattern formation, a fundamental process in biological development that facilitates the transformation of initially uniform or random states into spatially ordered structures.[277.1] A comprehensive understanding of these patterns is essential for unraveling the underlying principles of biological design and engineering.[277.1] Recent advancements in synthetic biology have the potential to overcome the limitations of traditional methods in studying these patterns, leading to innovative applications in various fields.[277.1] Specifically, synthetic biology is poised to contribute significantly to areas such as bioproduction, biosensing, and closed-loop therapeutic delivery, although many current developments remain confined to controlled laboratory settings and are not yet fully translatable to real-world applications.[277.1]In this section:
References
[1] Pattern Formation - an overview | ScienceDirect Topics — Introduction. Pattern formation is observed in many different prokaryotic systems. The patterns can be temporary such as those formed by swimming bacteria driven toward a chemoattractant , or more long-lasting such as the one-dimensional patterns of cells and heterocysts formed by some cyanobacteria , and the three-dimensional complex patterns formed by some bacteria in fruiting bodies
[6] Pattern formation - Wikipedia — In developmental biology, pattern formation refers to the generation of complex organizations of cell fates in space and time. In developmental biology, pattern formation describes the mechanism by which initially equivalent cells in a developing tissue in an embryo assume complex forms and functions. Embryogenesis, such as of the fruit fly Drosophila, involves coordinated control of cell fates. Pattern formation is genetically controlled, and often involves each cell in a field sensing and responding to its position along a morphogen gradient, followed by short distance cell-to-cell communication through cell signaling pathways to refine the initial pattern. This conceptual model was first described as the French flag model in the 1960s. More generally, the morphology of organisms is patterned by the mechanisms of evolutionary developmental biology, such as changing the timing and positioning of specific developmental events in the embryo.
[7] Generation and timing of graded responses to morphogen gradients — Morphogen gradients are known to subdivide a naive cell field into distinct zones of gene expression. ... Modeling of the dorsal gradient across species reveals interaction between embryo morphology and Toll signaling pathway ... twist and snail as positive and negative regulators during Drosophila mesoderm development. Genes Dev. 5, 1568-1576
[8] Forming and Interpreting Gradients in the Early Xenopus Embryo — The idea that a morphogen gradient activates the expression of different genes at different concentrations was perhaps stated most clearly by Wolpert's French flag model, in which a graded signal activates the expression of "blue," "white," and "red" genes at high, intermediate, and low concentrations (Wolpert 1969).Since that original work, great progress has been made in
[9] The interpretation of morphogen gradients | Development | The Company ... — Repressive interactions between morphogen-regulated genes are also important for gradient interpretation . A well-studied example is the contribution of cross repression to the partition of the Drosophila neuroectoderm into three columns along the DV axis (Cowden and Levine, 2003). This subdivision is mediated by three homeobox transcription
[10] Pattern Formation by Graded and Uniform Signals in the Early — Introduction. Early stages of Drosophila development rely on graded distributions of transcription factors in the precellular embryo. The anterior-to-posterior gradient of Bicoid (Bcd), a transcriptional activator, specifies the anterior body segments ().The ventral-to-dorsal nuclear localization gradient of Dorsal (Dl), which can both activate and repress gene expression, organizes the
[11] Pattern formation - Wikipedia — In developmental biology, pattern formation refers to the generation of complex organizations of cell fates in space and time. In developmental biology, pattern formation describes the mechanism by which initially equivalent cells in a developing tissue in an embryo assume complex forms and functions. Embryogenesis, such as of the fruit fly Drosophila, involves coordinated control of cell fates. Pattern formation is genetically controlled, and often involves each cell in a field sensing and responding to its position along a morphogen gradient, followed by short distance cell-to-cell communication through cell signaling pathways to refine the initial pattern. This conceptual model was first described as the French flag model in the 1960s. More generally, the morphology of organisms is patterned by the mechanisms of evolutionary developmental biology, such as changing the timing and positioning of specific developmental events in the embryo.
[16] Testing Turing's theory of morphogenesis in chemical cells — The Turing model of morphogenesis offers an explanation for how identical biological cells differentiate and change shape ( 1 ). It is difficult to overstate the impact Turing's model has had on developmental biology and the broad field of reaction-diffusion systems ( 2 - 9 ). The Turing model consists of two cases: The first, applicable for a ring of continuous material, has been
[17] The Chemical Basis of Morphogenesis - Wikipedia — Turing's paper explained how natural patterns, such as stripes, spots, and spirals, like those of the giant pufferfish, may arise. " The Chemical Basis of Morphogenesis " is an article that the English mathematician Alan Turing wrote in 1952. It describes how patterns in nature, such as stripes and spirals, can arise naturally from a homogeneous, uniform state. The theory, which can be
[19] A Second-Order Exponential Time Differencing Multi-step ... - Springer — The Swift-Hohenberg equation has been applied in the modeling of complex pattern formation , complex fluids and biological tissues . Simultaneously, it has extensive applications in many nonlinear science such as chemistry, biology, ecology, optics, and laser physics [ 22 , 44 , 55 ].
[51] Pattern formation - Nature — Pattern formation | Nature nature Alan Turing's 1952 paper on the origin of biological patterning1 solved an intellectual problem that had seemed so hopeless that it caused a great developmental biologist, Hans Driesch, to give up science and turn to the philosophy of vitalism. Although his proof was constructed analytically, Turing's paper contains the first computer simulations of pattern formation in the presence of stochastic fluctuations, and is possibly the first openly published case of computational experimentation. What Turing should receive credit for is opening the door to a new view of developmental biology, in which we deal directly with the chemical reactions and mechanical forces embryos use to self-organize their bodies from a single cell. Nature 482, 464 (2012).
[52] Mutation Examples in Animals and Their Impact — A prominent example involves the "Merle" gene, which leads to unique coat patterns characterized by patches of diluted pigment. However, this mutation can sometimes contribute to hearing loss or vision problems when present in double doses, illustrating how certain mutations can have both aesthetic and health-related consequences.
[53] How Genetic Mutations Create Unique Animal Traits — In nature, genetic mutations frequently occur and contribute to the evolutionary process. For example, the rich diversity of animal fur colors and patterns found in the wild is often the result of naturally occurring mutations that have been favored through natural selection. Fascinating Examples of Mutated Traits in Animals
[54] 12 Genetic Mutations That Have Shaped the Evolution of Species — Mutations leading to variations in skin coloration and patterns have enabled some species to blend in with their environment or mimic other species. This adaptation can deter predators or assist predators in ambushing prey, showcasing evolutionary strategies for survival through genetic changes.
[62] Turing Pattern Breakthroughs in Modern Biology — The mathematical framework provided by Turing's model allows scientists to simulate and predict pattern formation, offering a deeper understanding of underlying mechanisms. Recent studies have refined reaction diffusion theories, incorporating factors like environmental influences and genetic regulation.
[64] PDF — The English mathematician Alan Turing, in his 1952 article "The ChemicalBasis of Morphogenesis,"was the firstto propose a mathe-matical model for the formation of spatial patterns in biological systems. Turingclaimed that spatial patterns can arise as a result of instability in a reaction-diffusion-type mechanism for two chemicals (one acting as an activator and the other acting as an
[65] PDF — Philip K. Maini and Thomas E. Woolley Abstract How spatial patterning arises in biological systems is still an unresolved mystery. Here, we consider the first model for spatial pattern formation, proposed by Alan Turing, which showed that structure could emerge from processes that, in themselves, are non-patterning. He therefore went against the reductionist approach, arguing that biological
[66] Turing Pattern Breakthroughs in Modern Biology — Turing Pattern Breakthroughs in Modern Biology - BiologyInsights Explore the latest advancements in Turing patterns and their impact on understanding complex biological systems and developmental processes. These naturally occurring patterns are crucial for understanding complex biological processes and offer insights into how organisms develop and maintain structural diversity. The concept of reaction diffusion theories, introduced by Alan Turing in 1952, is foundational in understanding complex pattern emergence in biological systems. Integrating reaction diffusion models with genetic data allows better predictions and manipulation of spotted patterns, with applications in conservation biology. Turing patterns manifest in various biological contexts, offering insights into pattern formation mechanisms. Turing patterns are integral to understanding developmental biology, providing a framework for exploring how organisms develop complex structures.
[90] Pattern formation - Nature — Pattern formation | Nature nature Alan Turing's 1952 paper on the origin of biological patterning1 solved an intellectual problem that had seemed so hopeless that it caused a great developmental biologist, Hans Driesch, to give up science and turn to the philosophy of vitalism. Although his proof was constructed analytically, Turing's paper contains the first computer simulations of pattern formation in the presence of stochastic fluctuations, and is possibly the first openly published case of computational experimentation. What Turing should receive credit for is opening the door to a new view of developmental biology, in which we deal directly with the chemical reactions and mechanical forces embryos use to self-organize their bodies from a single cell. Nature 482, 464 (2012).
[101] [2302.13368] Phase-Field DeepONet: Physics-informed deep operator ... — Recent advances in scientific machine learning have shed light on the modeling of pattern-forming systems. However, simulations of real patterns still incur significant computational costs, which could be alleviated by leveraging large image datasets. Physics-informed machine learning and operator learning are two new emerging and promising concepts for this application. Here, we propose
[102] [2404.14987] Localized Multi-Dimensional Patterns - arXiv.org — There has been considerable progress in studying localized patterns over the past few decades, often by employing innovative mathematical tools and techniques. In particular, the study of localized pattern formation has benefited greatly from numerical techniques; the continuing advancement in computational power has helped to both identify new
[103] Advanced Computational Methods for Modeling, Prediction and ... — This paper provides a comprehensive review of recent advancements in computational methods for modeling, simulation, and optimization of complex systems in materials engineering, mechanical engineering, and energy systems. Since this paper reviews recent developments in artificial intelligence and computational methods focusing on the modeling, simulations, and optimization of complex systems in materials science, we should start by discussing emerging trends in AI, as now we can conduct virtual simulations that provide us with a depiction of the information landscape based on current knowledge. The modeling studies conducted in the works mentioned above, validated based on the experimental data sets, confirm the possibility of using practical artificial intelligence algorithms as advanced techniques for optimizing energy systems.
[104] Mathematical modeling of chondrogenic pattern formation during limb ... — The model proposed in not only explains the interactions between CG-1A and CG-8 to form spatial patterns of condensations during cell aggregation and bone formation but also provides the crucial insights of the pattern formation from a physical perspective that the limb skeletal patterning is a morphodynamic process and thus depends on
[107] Chapter 27 - Recent advances in computational modeling - ScienceDirect — The highest advancement in terms of tissue engineering is the design of "computational models" that are a potential guide in bioprinting and biomanufacturing technologies (Mozafari et al., 2019). Through this book chapter, an effort was made to discuss the advancement of computational biology in stem cell modeling and tissue engineering.
[121] Robust tissue pattern formation by coupling morphogen signal and cell ... — Recent advances in stem cell biology have enabled the development of 3D tissue culture systems called organoids, that mimic the cell composition and tissue morphology of their organ of origin. ... the design of synthetic genetic programs encoding cell-cell communication rules and testing their effect on the formation of tissue patterns (Davies
[122] Advancements in tissue and organ 3D bioprinting: Current techniques ... — Advancements in tissue and organ 3D bioprinting: Current techniques, applications, and future perspectives - ScienceDirect Advancements in tissue and organ 3D bioprinting: Current techniques, applications, and future perspectives The state-of-the-art of 3D bioprinting is comprehensively reviewed with emphasis on design and processing aspects. 3D bioprinting techniques have emerged as a flexible tool in tissue engineering and regenerative medicine to fabricate or pattern functional 3D bio-structures with precise geometric designs, bridging the divergence between engineered and natural tissue constructs. This review presents a picture of 3D bioprinting in the context of tissue engineering and regenerative medicine, with focus on biomaterials-related and design-centred aspects. Next article in issue No articles found. For all open access content, the relevant licensing terms apply.
[125] Turing Pattern Breakthroughs in Modern Biology — Turing Pattern Breakthroughs in Modern Biology - BiologyInsights Explore the latest advancements in Turing patterns and their impact on understanding complex biological systems and developmental processes. These naturally occurring patterns are crucial for understanding complex biological processes and offer insights into how organisms develop and maintain structural diversity. The concept of reaction diffusion theories, introduced by Alan Turing in 1952, is foundational in understanding complex pattern emergence in biological systems. Integrating reaction diffusion models with genetic data allows better predictions and manipulation of spotted patterns, with applications in conservation biology. Turing patterns manifest in various biological contexts, offering insights into pattern formation mechanisms. Turing patterns are integral to understanding developmental biology, providing a framework for exploring how organisms develop complex structures.
[126] Turing patterns with cellular computers: Cell Systems - Cell Press — Turing patterns are a key theoretical foundation for understanding organ development and organization. While they have been found to occur in natural systems, implementing new biological systems that form Turing patterns has remained challenging. To address this, Tica et al. used synthetic genetic networks to engineer living cellular computers that successfully generate Turing patterns within
[127] A Comprehensive Network Atlas Reveals That Turing Patterns Are Common ... — Turing patterns are stable spatial patterns resulting from the interplay of chemical reactions and molecular diffusion and underlie many developmental processes. Here, we perform an exhaustive analysis of potential Turing pattern generating mechanisms for systems with two or three molecular species. The resulting atlas contains the blueprints of Turing pattern generating mechanisms, and shows
[128] Turing's model for biological pattern formation and the robustness ... — Postulating plausible theoretical models of biological heterogeneity is not only difficult, but it is also further complicated by the problem of generating robustness, i.e. once we can generate a pattern, how do we ensure that this pattern is consistently reproducible in the face of perturbations to the domain, reaction time scale, boundary conditions and so forth. Hence, gene-expression time delays can be readily incorporated into Turing models on stationary domains for Gierer–Meinhardt kinetics and this is readily generalized for both growing domains and other Turing systems, as further motivated and illustrated in Gaffney & Monk , Seirin-Lee et al. In addition, gene-expression time delays sensitize the timing of the onset of patterning to fluctuations in the initial conditions for ligand internalization models on growing domains .
[129] Pattern formation - Wikipedia — In developmental biology, pattern formation refers to the generation of complex organizations of cell fates in space and time. In developmental biology, pattern formation describes the mechanism by which initially equivalent cells in a developing tissue in an embryo assume complex forms and functions. Embryogenesis, such as of the fruit fly Drosophila, involves coordinated control of cell fates. Pattern formation is genetically controlled, and often involves each cell in a field sensing and responding to its position along a morphogen gradient, followed by short distance cell-to-cell communication through cell signaling pathways to refine the initial pattern. This conceptual model was first described as the French flag model in the 1960s. More generally, the morphology of organisms is patterned by the mechanisms of evolutionary developmental biology, such as changing the timing and positioning of specific developmental events in the embryo.
[131] Pattern Formation - an overview | ScienceDirect Topics — Pattern formation in secondary fields such as a developing limb then occurred in four basic stages: (1) cells that make up the field are defined; (2) specific signaling centers are established within the field to provide positional information; (3) the positional information is recorded on a cell by cell basis; and (4) cells differentiate in response to additional cues according to the encoded positional information. (1) The position-dependent class (p producing s) involves (a) the positional information subclass, as determined by gradient models, polar coordinate models, or the progress zone model; (b) the prepattern subclass, for which there are physical force models, reaction–diffusion models and induction models; (c) the determination wave subclass, for which there are chemical wave models (Belousov–Zhabotinsky reaction), the sequential induction model, the clock and wave-front model, and inhibitory field and competence wave models; and (d) the Darwinian subclass, with cell death and state change models.
[132] Pattern Formation and Complexity in Single Cells - PMC — The question now is to what extent did early animal evolution rely on subcellular patterning mechanisms versus newly evolved cell-cell communication pathways. Studying the mechanisms of pattern formation and complexity in single cells may thus hold the key to understanding how plants and animals evolved. Acknowledgments
[133] Models of Biological Pattern Formation: From Elementary Steps to the ... — Hydra was originally chosen as a model system to get insights into basic mechanisms underlying biological pattern formation. More recent modeling suggests that this radially-symmetric animal can also provide key insights into the establishment of a secondary axis and the evolution of the bilateral body plan of higher animals.
[136] Genetic variation - Definition, Types, Causes, Examples — Genetic variation - Definition, Types, Causes, Examples - Biology Notes Online Genetic variation – Definition, Types, Causes, Examples Genetic variation refers to the diversity in DNA sequences among individuals within a population. In the human population, examples of genetic variation can be seen in traits such as hair color, dimples, and blood type. Genetic variation refers to the differences in DNA sequences among individuals within a population, resulting in diverse traits. Genetic variation is essential for the adaptability and evolution of species, and it arises from several key factors that introduce diversity into the genetic makeup of populations. Genetic variation manifests in numerous examples across different organisms, showcasing the adaptability and diversity inherent in biological populations.
[139] Shaping up with morphogen gradients | Nature Cell Biology — Depending on the cell's position within this morphogen gradient, it will experience a difference in morphogen concentration and will respond to that by differentiating into a specific cell type 1.
[141] Morphogen interpretation: concentration, time, competence, and ... — Spatial gradients in morphogen production can also emerge from the displacement of cells during development, especially, in growing tissues.63, 64, 65 This is for example the case for FGF8 during vertebrate axis elongation.63 Here, transcription of fgf8 mRNA is restricted to the posterior tip of the embryo (Figure 2(c) and (d)).
[142] Genetic and Molecular Analysis of Pattern Formation Processes in Drosophila — A detailed understanding of the processes controlling Drosophila development has become possible by a systematic genetic analysis of mutations leading to pattern defects during embryogenesis. It was possible to obtain definitive proof for the involvement of
[144] The Toll gene in Drosophila pattern formation - PubMed — The analysis of Toll by Kathryn Anderson in my laboratory in Tübingen and subsequently in her own laboratory in Berkeley singled out Toll as a central component of the complex pathway regulating dorsoventral polarity and pattern of the Drosophila embryo.
[145] Spontaneous motor-behavior abnormalities in two Drosophila models of ... — Mutations in hundreds of genes cause neurodevelopmental disorders with abnormal motor behavior alongside cognitive deficits. Boys with fragile X syndrome (FXS), a leading monogenic cause of intellectual disability, often display repetitive behaviors, a core feature of autism. By direct observation a …
[158] Morphogen gradients in Development: from form to function — More commonly, morphogens comprise secreted proteins that form an extracellular gradient across a field of cells. Morphogens can consist of cytoplasmic proteins, such as transcription factors that form a gradient by diffusion within a single cell or syncytium, or secreted signaling molecules that travel from cell to cell. A more common mechanism of gradient formation in development is the locally restricted transcription of a gene encoding a secreted protein, followed by movement of the signaling molecule across or through a field of cells. At first glance, formation of an extracellular gradient seems to be a simple matter of free diffusion of the morphogen away from its source followed by degradation, either outside of receiving cells or following receptor activation and internalization.
[161] Morphogen gradients: from generation to interpretation — Abstract Morphogens are long-range signaling molecules that pattern developing tissues in a concentration-dependent manner. The graded activity of morphogens within tissues exposes cells to different signal levels and leads to region-specific transcriptional responses and cell fates. In its simplest incarnation, a morphogen signal forms a gradient by diffusion from a local source and clearance
[162] Morphogen Gradients, in Theory: Developmental Cell — The idea that morphogen gradients are established by a process of repeated cycles of exocytosis and endocytosis—so-called planar transcytosis—has been gaining acceptance. This is now challenged by a theoretical approach that experimental biologists should not dismiss; diffusive mechanisms of gradient formation may be correct after all.
[163] The interpretation of morphogen gradients | Development | The Company ... — Although the morphogen concept has provided an enduring and valid framework for understanding pattern formation, it raises many mechanistic issues. Much attention has focused on how the distribution of a morphogen through a tissue establishes and maintains a gradient of activity (Vincent and Dubois, 2002; Tabata and Takei, 2004);however, how the signal is perceived and interpreted in a graded
[177] PDF — beginning with Turing's idea and the theoretical framework of his reaction-diffusion equations. Then, we will discuss how patterns form from a homogeneous system and the mechanisms behind which patterns will develop. Next, we introduce Turing's original mathematical model and how each parameter affects the formation of patterns, or lack
[185] Pattern formation - Nature — Pattern formation | Nature nature Alan Turing's 1952 paper on the origin of biological patterning1 solved an intellectual problem that had seemed so hopeless that it caused a great developmental biologist, Hans Driesch, to give up science and turn to the philosophy of vitalism. Although his proof was constructed analytically, Turing's paper contains the first computer simulations of pattern formation in the presence of stochastic fluctuations, and is possibly the first openly published case of computational experimentation. What Turing should receive credit for is opening the door to a new view of developmental biology, in which we deal directly with the chemical reactions and mechanical forces embryos use to self-organize their bodies from a single cell. Nature 482, 464 (2012).
[186] A Modern View on Turing's Theory of Pattern Formation — Nearly seventy years ago Alan Turing, a pioneer of Computer Science, developed a theory to explain how certain patterns in nature could arise spontaneously from simple chemical systems. This idea was a significant departure from much of his previous work on the theory of computation, and used very different kinds of mathematics.
[188] The old and new faces of morphology: the legacy of D'Arcy Thompson's ... — In 1917, the publication of On Growth and Form by D'Arcy Wentworth Thompson challenged both mathematicians and naturalists to think about biological shapes and diversity as more than a confusion of chaotic forms generated at random, but rather as geometric shapes that could be described by principles of physics and mathematics. Thompson's work was based on the ideas of Galileo and Goethe on
[190] Formation and deformation of patterns through diffusion — Simulating various patterns exhibited on biological forms with mathematical models has become an important supplement to theoretical biology. ... such as temperature, affect the diffusion rates of corresponding morphogenes which, in turn, alter a basic pattern to certain extent. ... "A model of pattern formation in insect embryogenesis", J
[191] Influence of temperature on Turing pattern formation — 1. Introduction. In the decades since Turing [] first described the emergence of spatial instability and resulting pattern formation in reaction-diffusion systems, the eponymous Turing instability has become a popular mechanism for investigating pattern formation in biological, chemical and physical systems [2-8].Experimental work suggests that temperature differences can and do change
[192] The Role of Mathematical Models in Understanding Pattern Formation in ... — The Role of Mathematical Models in Understanding Pattern Formation in Developmental Biology - PMC Development of an organism such as a human that contains many interacting components involves numerous complex processes, including signal transduction, gene expression, pattern formation, transport of material, growth, and mechanical forces, and thus, it is not surprising that mathematical models and analysis have played a role in understanding development. In the context of pattern formation, the spatial distribution of extracellular state variables to which the cells in a developing tissue respond is called the morphogenetic landscape, and when the signals are diffusible molecules that affect the internal state in a concentration-dependent manner, they are called morphogens, a term coined by the British mathematician Alan Turing (Turing 1952).
[193] Yeast Colonies: Patterns, Growth, and Genetic Factors — Yeast colony patterns emerge from genetic mechanisms controlling adhesion, differentiation, and spatial organization. These patterns optimize resource use and environmental adaptation. Genes like FLO11 in Saccharomyces cerevisiae influence structured colony formation by promoting cell-cell interactions and surface attachment.
[194] PDF — The Reaction-Diffusion Equations Reaction-diffusion (RD) equations arise naturally in systems consisting of many interacting components, (e.g., chemical reactions) and are widely used to describe pattern-formation phenomena in variety of biological, chemical and physical sys-tems. The principal ingredients of all these models are equation of the form
[195] Analysis of Coupled Reaction-Diffusion Equations for RNA Interactions — We consider a system of coupled reaction-diffusion equations that models the interaction between multiple types of chemical species, particularly the interaction between one messenger RNA and different types of non-coding microRNAs in biological cells.
[196] Chemotactic effects in reaction-diffusion equations for inflammation — The reaction-diffusion system combines reactions f (q) between the species or concerning a single species with spatial diffusion of the species D Δ q. With the aim to describe liver infections, we can interpret the reaction-diffusion system as a predator-prey system with additional diffusion effects.
[198] Advances and challenges in programming pattern formation using living ... — A classical model of self-organized pattern formation is the Turing model, which consists of long-range inhibition and short-range activation. Due to its ability to generate diverse periodic patterns, such as spots and strips, the Turing model has been invoked to explain pattern formation in several biological contexts 26 - 28 and explored
[199] Pattern formation by dynamically interacting network motifs — Based on the combination of computational analysis and genetic experiments, we show that the model accounts for the key features of wild-type pattern formation, correctly predicts patterning defects in multiple mutants, and guides the identification of additional regulatory links in a complex pattern formation mechanism.
[203] PDF — A further example used to study pattern formation is the Gray-Scott model for autocatalysis in the continuously fed unstirred flow reactor which may exhibit bistability. The kinetic scheme for this reaction is a variant of the autocatalytic model for glycolytic oscillations proposed by Sel'kov . The scheme considers the
[204] Mathematical modeling of chondrogenic pattern formation during limb ... — Mathematical modeling of chondrogenic pattern formation during limb development: Recent advances in continuous models - ScienceDirect Mathematical modeling of chondrogenic pattern formation during limb development: Recent advances in continuous models We include a list of gene products that are relevant to mathematical models of chondrogenic pattern formation in the limb. Correspondingly, there are two classes of mathematical models of limb development: Those concerned with modeling the growth of the limb buds and those that model the process of pattern formation of pre-skeletal cartilage within the developing buds. To investigate the mechanisms of limb development and pattern formation, mathematical modeling is extremely useful.
[205] The Role of Mathematical Models in Understanding Pattern Formation in ... — The Role of Mathematical Models in Understanding Pattern Formation in Developmental Biology - PMC Development of an organism such as a human that contains many interacting components involves numerous complex processes, including signal transduction, gene expression, pattern formation, transport of material, growth, and mechanical forces, and thus, it is not surprising that mathematical models and analysis have played a role in understanding development. In the context of pattern formation, the spatial distribution of extracellular state variables to which the cells in a developing tissue respond is called the morphogenetic landscape, and when the signals are diffusible molecules that affect the internal state in a concentration-dependent manner, they are called morphogens, a term coined by the British mathematician Alan Turing (Turing 1952).
[206] Biology by numbers: mathematical modelling in developmental biology ... — In recent years, mathematical modelling of developmental processes has earned new respect. Not only have mathematical models been used to validate hypotheses made from experimental data, but
[217] Pattern Formation - an overview | ScienceDirect Topics — Pattern formation in secondary fields such as a developing limb then occurred in four basic stages: (1) cells that make up the field are defined; (2) specific signaling centers are established within the field to provide positional information; (3) the positional information is recorded on a cell by cell basis; and (4) cells differentiate in response to additional cues according to the encoded positional information. (1) The position-dependent class (p producing s) involves (a) the positional information subclass, as determined by gradient models, polar coordinate models, or the progress zone model; (b) the prepattern subclass, for which there are physical force models, reaction–diffusion models and induction models; (c) the determination wave subclass, for which there are chemical wave models (Belousov–Zhabotinsky reaction), the sequential induction model, the clock and wave-front model, and inhibitory field and competence wave models; and (d) the Darwinian subclass, with cell death and state change models.
[219] Epigenetic regulation of early human embryo development — Studies of mammalian development have advanced our understanding of the genetic, epigenetic, and cellular processes that orchestrate embryogenesis and have uncovered new insights into the unique aspects of human embryogenesis. Recent studies have now produced the first epigenetic maps of early human embryogenesis, stimulating new ideas about
[220] The establishment and regulation of human germ cell lineage — The specification of primordial germ cells (PGCs) during early embryogenesis initiates the development of the germ cell lineage that ensures the perpetuation of genetic and epigenetic information from parents to offspring. Defects in germ cell development may lead to infertility or birth defects. Historically, our understanding of human PGCs (hPGCs) regulation has primarily been derived from
[224] Self-organization: the fundament of cell biology - PMC — Self-organization: the fundament of cell biology - PMC It therefore comes as no surprise that many properties and features of self-organized systems, such as spontaneous formation of patterns, nonlinear coupling of reactions, bi-stable switches, waves and oscillations, are found in all aspects of modern cell biology. This article is part of the theme issue ‘Self-organization in cell biology’. It therefore comes as no surprise that many properties and features of self-organized systems, such as spontaneous formation of patterns, nonlinear coupling of reactions, bi-stable switches, waves and oscillations, are found in all aspects of modern cell biology. This theme issue on self-organization in cell biology aims to summarize current approaches and identify future challenges in the study and application of self-organization in natural and synthetic biological systems.
[231] Turing Pattern Breakthroughs in Modern Biology — Turing Pattern Breakthroughs in Modern Biology - BiologyInsights Explore the latest advancements in Turing patterns and their impact on understanding complex biological systems and developmental processes. These naturally occurring patterns are crucial for understanding complex biological processes and offer insights into how organisms develop and maintain structural diversity. The concept of reaction diffusion theories, introduced by Alan Turing in 1952, is foundational in understanding complex pattern emergence in biological systems. Integrating reaction diffusion models with genetic data allows better predictions and manipulation of spotted patterns, with applications in conservation biology. Turing patterns manifest in various biological contexts, offering insights into pattern formation mechanisms. Turing patterns are integral to understanding developmental biology, providing a framework for exploring how organisms develop complex structures.
[264] Pattern formation in biology: a comparison of models and experiments — Abstract How are the complex structures of a higher organism generated in such a reproducible way? Models of biological pattern formation are given in the form of nonlinear partial differential equations that describe production and decay rates as well as the diffusion of substances involved in pattern formation. As shown by comparison between expected and observed regulatory behaviour, these
[266] The Role of Mathematical Models in Understanding Pattern Formation in ... — The Role of Mathematical Models in Understanding Pattern Formation in Developmental Biology - PMC Development of an organism such as a human that contains many interacting components involves numerous complex processes, including signal transduction, gene expression, pattern formation, transport of material, growth, and mechanical forces, and thus, it is not surprising that mathematical models and analysis have played a role in understanding development. In the context of pattern formation, the spatial distribution of extracellular state variables to which the cells in a developing tissue respond is called the morphogenetic landscape, and when the signals are diffusible molecules that affect the internal state in a concentration-dependent manner, they are called morphogens, a term coined by the British mathematician Alan Turing (Turing 1952).
[268] Turing's model for biological pattern formation and the robustness ... — Postulating plausible theoretical models of biological heterogeneity is not only difficult, but it is also further complicated by the problem of generating robustness, i.e. once we can generate a pattern, how do we ensure that this pattern is consistently reproducible in the face of perturbations to the domain, reaction time scale, boundary conditions and so forth. Hence, gene-expression time delays can be readily incorporated into Turing models on stationary domains for Gierer–Meinhardt kinetics and this is readily generalized for both growing domains and other Turing systems, as further motivated and illustrated in Gaffney & Monk , Seirin-Lee et al. In addition, gene-expression time delays sensitize the timing of the onset of patterning to fluctuations in the initial conditions for ligand internalization models on growing domains .
[276] Synthetic Pattern Formation | Biochemistry - ACS Publications — A fundamental question in biology is how biological patterns emerge. Because of the presence of numerous confounding factors, it is tremendously challenging to elucidate the mechanisms underlying pattern formation solely on the basis of studies of natural biological systems. Synthetic biology provides a complementary approach to investigating pattern formation by creating systems that are
[277] Deciphering the Code of Pattern Formation: Integrating In Silico and ... — Pattern formation is a fundamental process in biological development, enabling the transformation of initially uniform or random states into spatially ordered structures. A comprehensive understanding of the formation and function of these patterns is crucial for unraveling the underlying principles of biological design and engineering. In recent years, synthetic biology has emerged as a
[278] Engineering synthetic spatial patterns in microbial populations and ... — Spatial pattern formation is an important feature of almost all biological systems. Thanks to the advances in synthetic biology, we can engineer microbial populations and communities to display sophisticated spatial patterns. This bottom-up approach can be used to elucidate the general principles underlying pattern formation.
[279] Synthetic biology: a new approach to study biological pattern formation ... — Using periodic stripe pattern formation as a paradigm, we discuss how to apply synthetic biology in understanding biological pattern formation and hereafter foster the applications like tissue engineering.
[298] Applications, challenges, and needs for employing synthetic biology ... — Advertisement View all journals Search Log in Explore content About the journal Publish with us Sign up for alerts RSS feed nature nature communications perspectives article Applications, challenges, and needs for employing synthetic biology beyond the lab Download PDF Download PDF Perspective Open access Published: 02 March 2021 Applications, challenges, and needs for employing synthetic biology beyond the lab Sierra M. Brooks ORCID: orcid.org/0000-0002-6914-25041 & Hal S. Alper ORCID: orcid.org/0000-0002-8246-86051,2 Nature Communications volume 12, Article number: 1390 (2021) Cite this article 51k Accesses 62 Altmetric Metrics details Subjects Biotechnology Synthetic biology Abstract Synthetic biology holds great promise for addressing global needs. However, most current developments are not immediately translatable to ‘outside-the-lab’ scenarios that differ from controlled laboratory settings. Here we analyze recent advances in developing synthetic biological platforms for outside-the-lab scenarios with a focus on three major application spaces: bioproduction, biosensing, and closed-loop therapeutic and probiotic delivery. We focus this Perspective on three major application spaces for the outside-the-lab deployment of synthetic biology: bioproduction, biosensing, and closed-loop living therapeutic and probiotic delivery.