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Register a new userBeyond activator-inhibitor networks: the generalised Turing mechanism
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The Turing patterning mechanism is believed to underly the formation of repetitive structures in development, such as zebrafish stripes and mammalian digits, but it has proved difficult to isolate the specific biochemical species responsible for pattern formation. Meanwhile, synthetic biologists have designed Turing systems for implementation in cell colonies, but none have yet led to visible patterns in the laboratory. In both cases, the relationship between underlying chemistry and emergent biology remains mysterious. To help resolve the mystery, this article asks the question: what kinds of biochemical systems can generate Turing patterns? We find general conditions for Turing pattern inception -- the ability to generate unstable patterns from random noise -- which may lead to the ultimate formation of stable patterns, depending on biochemical non-linearities. We find that a wide variety of systems can generate stable Turing patterns, including several which are currently unknown, such as two-species systems composed of two self-activators, and systems composed of a short-range inhibitor and a long-range activator. We furthermore find that systems which are widely believed to generate stable patterns may in fact only generate unstable patterns, which ultimately converge to spatially-homogeneous concentrations. Our results suggest that a much wider variety of systems than is commonly believed could be responsible for observed patterns in development, or could be good candidates for synthetic patterning networks.
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An understanding of the underlying mechanism of side--branching is paramount in controlling and/or therapeutically treating mammalian organs, such as lungs, kidneys, and glands. Motivated by an activator-inhibitor-substrate approach that is conjectured to dominate the initiation of side--branching in pulmonary vascular pattern, I demonstrate a distinct transverse front instability in which new fingers grow out of an oscillatory breakup dynamics at the front line, without any typical length scale. These two features are attributed to unstable peak solutions in 1D that subcritically emanate from the Turing bifurcation and that exhibit repulsive interactions. The results are based on a bifurcation analysis and numerical simulations, and provide a potential strategy toward developing a framework of side--branching also of other biological systems, such as plant roots and cellular protrusions.
A theory for diffusivity estimation for spatially extended activator-inhibitor dynamics modelling the evolution of intracellular signaling networks is developed in the mathematical framework of stochastic reaction-diffusion systems. In order to account for model uncertainties, we extend the results for parameter estimation for semilinear stochastic partial differential equations, as developed in [PS20], to the problem of joint estimation of diffusivity and parametrized reaction terms. Our theoretical findings are applied to the estimation of effective diffusivity of signaling components contributing to intracellular dynamics of the actin cytoskeleton in the model organism Dictyostelium discoideum.
Although accumulation of molecular damage is suggested to be an important molecular mechanism of aging, a quantitative link between the dynamics of damage accumulation and mortality of species has so far remained elusive. To address this question, we examine stability properties of a generic gene regulatory network (GRN) and demonstrate that many characteristics of aging and the associated population mortality rate emerge as inherent properties of the critical dynamics of gene regulation and metabolic levels. Based on the analysis of age-dependent changes in gene-expression and metabolic profiles in Drosophila melanogaster, we explicitly show that the underlying GRNs are nearly critical and inherently unstable. This instability manifests itself as aging in the form of distortion of gene expression and metabolic profiles with age, and causes the characteristic increase in mortality rate with age as described by a form of the Gompertz law. In addition, we explain late-life mortality deceleration observed at very late ages for large populations. We show that aging contains a stochastic component, related to accumulation of regulatory errors in transcription/translation/metabolic pathways due to imperfection of signaling cascades in the network and of responses to environmental factors. We also establish that there is a strong deterministic component, suggesting genetic control. Since mortality in humans, where it is characterized best, is strongly associated with the incidence of age-related diseases, our findings support the idea that aging is the driving force behind the development of chronic human diseases.
Excitable pulses are among the most widespread dynamical patterns that occur in many different systems, ranging from biological cells to chemical reactions and ecological populations. Traditionally, the mutual annihilation of two colliding pulses is regarded as their prototypical signature. Here we show that colliding excitable pulses may exhibit soliton-like crossover and pulse nucleation if the system obeys a mass conservation constraint. In contrast to previous observations in systems without mass conservation, these alternative collision scenarios are robustly observed over a wide range of parameters. We demonstrate our findings using a model of intracellular actin waves since, on time scales of wave propagations over the cell scale, cells obey the conservation of actin monomers. The results provide a key concept to understand the ubiquitous occurrence of actin waves in cells, suggesting why they are so common, and why their dynamics is robust and long-lived.
Cancer is increasingly perceived as a systems-level, network phenomenon. The major trend of malignant transformation can be described as a two-phase process, where an initial increase of network plasticity is followed by a decrease of plasticity at late stages of tumor development. The fluctuating intensity of stress factors, like hypoxia, inflammation and the either cooperative or hostile interactions of tumor inter-cellular networks, all increase the adaptation potential of cancer cells. This may lead to the bypass of cellular senescence, and to the development of cancer stem cells. We propose that the central tenet of cancer stem cell definition lies exactly in the indefinability of cancer stem cells. Actual properties of cancer stem cells depend on the individual stress-history of the given tumor. Cancer stem cells are characterized by an extremely large evolvability (i.e. a capacity to generate heritable phenotypic variation), which corresponds well with the defining hallmarks of cancer stem cells: the possession of the capacity to self-renew and to repeatedly re-build the heterogeneous lineages of cancer cells that comprise a tumor in new environments. Cancer stem cells represent a cell population, which is adapted to adapt. We argue that the high evolvability of cancer stem cells is helped by their repeated transitions between plastic (proliferative, symmetrically dividing) and rigid (quiescent, asymmetrically dividing, often more invasive) phenotypes having plastic and rigid networks. Thus, cancer stem cells reverse and replay cancer development multiple times. We describe network models potentially explaining cancer stem cell-like behavior. Finally, we propose novel strategies including combination therapies and multi-target drugs to overcome the Nietzschean dilemma of cancer stem cell targeting: what does not kill me makes me stronger.
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