scholarly journals The people behind the papers – Andrew Economou and Jeremy Green

Development ◽  
2020 ◽  
Vol 147 (20) ◽  
pp. dev197293
Keyword(s):  
Developmental Biology ◽  
Perturbation Analysis ◽  
Reaction Diffusion ◽  
Biological Complexity ◽  
Periodic Patterns ◽  
Alan Turing ◽  
King's College ◽  
The People

ABSTRACTInteracting morphogens produce periodic patterns in developing tissues. Such patterning can be modelled as reaction-diffusion (RD) processes (as originally formulated by Alan Turing), and although these models have been developed and refined over the years, they often tend to oversimplify biological complexity by restricting the number of interacting morphogens. A new paper in Development reports how perturbation analysis can guide multi-morphogen modelling of the striped patterning the roof of the mouse mouth. To hear more about the story, we caught up with first author Andrew Economou and his former supervisor Jeremy Green, Professor of Developmental Biology at King's College, London.

scholarly journals Perturbation analysis of a multi-morphogen Turing reaction-diffusion stripe patterning system reveals key regulatory interactions

Development ◽  
2020 ◽  
Vol 147 (20) ◽  
pp. dev190553
Author(s):  
Andrew D. Economou ◽  
Nicholas A. M. Monk ◽  
Jeremy B. A. Green
Keyword(s):  
Perturbation Analysis ◽  
Reaction Diffusion ◽  
Regulatory Interactions ◽  
The People ◽  
Molecular Events ◽  
Experimental Constraint ◽  
Fgf Signalling ◽  
Analytical Approaches ◽  
Minimal Networks

ABSTRACTPeriodic patterning is widespread in development and can be modelled by reaction-diffusion (RD) processes. However, minimal two-component RD descriptions are vastly simpler than the multi-molecular events that actually occur and are often hard to relate to real interactions measured experimentally. Addressing these issues, we investigated the periodic striped patterning of the rugae (transverse ridges) in the mammalian oral palate, focusing on multiple previously implicated pathways: FGF, Hh, Wnt and BMP. For each, we experimentally identified spatial patterns of activity and distinct responses of the system to inhibition. Through numerical and analytical approaches, we were able to constrain substantially the number of network structures consistent with the data. Determination of the dynamics of pattern appearance further revealed its initiation by ‘activators’ FGF and Wnt, and ‘inhibitor’ Hh, whereas BMP and mesenchyme-specific-FGF signalling were incorporated once stripes were formed. This further limited the number of possible networks. Experimental constraint thus limited the number of possible minimal networks to 154, just 0.004% of the number of possible diffusion-driven instability networks. Together, these studies articulate the principles of multi-morphogen RD patterning and demonstrate the utility of perturbation analysis for constraining RD systems.This article has an associated ‘The people behind the papers’ interview.

scholarly journals The periodic coloration in birds forms through a prepattern of somite origin

Science ◽  
2018 ◽  
Vol 361 (6408) ◽  
pp. eaar4777 ◽  
Author(s):  
Nicolas Haupaix ◽  
Camille Curantz ◽  
Richard Bailleul ◽  
Samantha Beck ◽  
Annie Robic ◽  
...  
Keyword(s):  
Expression Profile ◽  
Natural Variation ◽  
Reaction Diffusion ◽  
Positional Information ◽  
Pigment Production ◽  
Periodic Patterns ◽  
Local Dynamics ◽  
Step Process ◽  
Early Developmental ◽  
Dose Dependent

The periodic stripes and spots that often adorn animals’ coats have been largely viewed as self-organizing patterns, forming through dynamics such as Turing’s reaction-diffusion within the developing skin. Whether preexisting positional information also contributes to the periodicity and orientation of these patterns has, however, remained unclear. We used natural variation in colored stripes of juvenile galliform birds to show that stripes form in a two-step process. Autonomous signaling from the somite sets stripe position by forming a composite prepattern marked by the expression profile of agouti. Subsequently, agouti regulates stripe width through dose-dependent control of local pigment production. These results reveal that early developmental landmarks can shape periodic patterns upstream of late local dynamics, and thus constrain their evolution.

Radiolaria: validating the Turing theory

2017 ◽  
Author(s):  
Bernard Richards
Keyword(s):  
Diffusion Mechanism ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Black And White ◽  
Alan Turing ◽  
School Sports ◽  
The University ◽  
University Of Manchester

In his 1952 paper ‘The chemical basis of morphogenesis’ Turing postulated his now famous Morphogenesis Equation. He claimed that his theory would explain why plants and animals took the shapes they did. When I joined him, Turing suggested that I might solve his equation in three dimensions, a new problem. After many manipulations using rather sophisticated mathematics and one of the first factory-produced computers in the UK, I derived a series of solutions to Turing’s equation. I showed that these solutions explained the shapes of specimens of the marine creatures known as Radiolaria, and that they corresponded very closely to the actual spiny shapes of real radiolarians. My work provided further evidence for Turing’s theory of morphogenesis, and in particular for his belief that the external shapes exhibited by Radiolaria can be explained by his reaction–diffusion mechanism. While working in the Computing Machine Laboratory at the University of Manchester in the early 1950s, Alan Turing reignited the interests he had had in both botany and biology from his early youth. During his school-days he was more interested in the structure of the flowers on the school sports field than in the games played there (see Fig. 1.3). It is known that during the Second World War he discussed the problem of phyllotaxis (the arrangement of leaves and florets in plants), and then at Manchester he had some conversations with Claude Wardlaw, the Professor of Botany in the University. Turing was keen to take forward the work that D’Arcy Thompson had published in On Growth and Form in 1917. In his now-famous paper of 1952 Turing solved his own ‘Equation of Morphogenesis’ in two dimensions, and demonstrated a solution that could explain the ‘dappling’—the black-and-white patterns—on cows. The next step was for me to solve Turing’s equation in three dimensions. The two-dimensional case concerns only surface features of organisms, such as dappling, spots, and stripes, whereas the three-dimensional version concerns the overall shape of an organism. In 1953 I joined Turing as a research student in the University of Manchester, and he set me the task of solving his equation in three dimensions. A remarkable journey of collaboration began. Turing chatted to me in a very friendly fashion.

scholarly journals Letter to Turing

2018 ◽  
Vol 36 (6) ◽  
pp. 73-94 ◽  
Author(s):  
Giuseppe Longo
Keyword(s):  
Scientific Method ◽  
Reaction Diffusion ◽  
Neural Nets ◽  
Scientific Letter ◽  
Alan Turing ◽  
Diffusion Dynamics ◽  
Human Attitude ◽  
Scientific Quest ◽  
The Impact ◽  
Made In

This personal, yet scientific, letter to Alan Turing, reflects on Turing's personality in order to better understand his scientific quest. It then focuses on the impact of his work today. By joining human attitude and particular scientific method, Turing is able to “immerse himself” into the phenomena on which he works. This peculiar blend justifies the epistolary style. Turing makes himself a “human computer”, he lives the dramatic quest for an undetectable imitation of a man, a woman, a machine. He makes us see the continuous deformations of a material action/reaction/diffusion dynamics of hardware with no software. Each of these investigations opens the way to new scientific paths with major consequences for contemporary live and for knowledge. The uses and the effects of these investigations will be discussed: the passage from classical AI to today's neural nets, the relevance of non-linearity in biological dynamics, but also their abuses, such as the myth of a computational world, from a Turing-machine like universe to an encoded homunculus in the DNA. It is shown that these latter ideas, which are sometimes even made in Turing's name, contradict his views.

scholarly journals Spatially periodic calcium profiles around single channels

2016 ◽  
Author(s):  
S. L. Mironov
Keyword(s):  
Calcium Binding ◽  
Linear Models ◽  
Single Channel ◽  
Reaction Diffusion ◽  
Diffusion Problem ◽  
Cell Physiology ◽  
Single Channels ◽  
Periodic Patterns ◽  
Calcium Diffusion ◽  
Spatially Periodic

AbstractThe concept of calcium nanodomains established around the sites of calcium entry into the cell is fundamental for mechanistic consideration of key physiological responses. It stems from linear models of calcium diffusion from single channel into the cytoplasm, but is only valid for calcium increases smaller than the concentration of calcium-binding species. Recent experiments indicate much higher calcium levels in the vicinity of channel exit that should cause buffer saturation. I here derive explicit solutions of respective non-linear reaction-diffusion problem and found dichotomous solution - for small fluxes the steady state calcium profiles have quasi-exponential form, whereas in the case of buffer saturation calcium distributions show spatial periodicity. These non-trivial and novel spatial calcium profiles are supported by Monte-Carlo simulations. Imaging of 1D- and radial distributions around single α-synuclein channels measured in cell-free conditions supports the theory. I suggest that periodic patterns may arise under different physiological conditions and play specific role in cell physiology.

scholarly journals Perturbation analysis of a multi-morphogen Turing Reaction-Diffusion stripe patterning system reveals key regulatory interactions

2019 ◽  
Author(s):  
Andrew D. Economou ◽  
Nicholas A.M. Monk ◽  
Jeremy B.A. Green
Keyword(s):  
Network Topology ◽  
Perturbation Analysis ◽  
Reaction Diffusion ◽  
Signalling Pathways ◽  
Core Network ◽  
Pathway Network ◽  
Regulatory Interactions ◽  
Two Component ◽  
Network Topologies ◽  
Phase Relationships

AbstractPeriodic patterning is extremely widespread in developmental biology and is broadly modelled by Reaction-Diffusion (RD) processes. However, the minimal two-component RD system is vastly simpler than the multimolecular events that current biology is now able to describe. Moreover, RD models are typically underconstrained such that it is often hard to meaningfully relate the model architecture to real interactions measured experimentally. To address both these issues, we investigated the periodic striped patterning of the rugae (transverse ridges) in the roof of the mammalian palate. We experimentally implicated a small number of major signalling pathways and established theoretical limits on the number of pathway network topologies that can account for the stable spatial phase relationships of their observed signalling outputs. We further conducted perturbation analysis both experimentally and in silico, critically to assess the effects of perturbations on established patterns. We arrived at a relatively highly-constrained number of possible networks and found that these share some common motifs. Finally, we examined the dynamics of pattern appearance and discovered a core network consisting of epithelium-specific FGF and Wnt as mutually antagonistic “activators” and Shh as the “inhibitor”, which initiates the periodicity and whose existence constrains the network topology still further. Together these studies articulate the principles of multi-morphogen RD patterning and demonstrate the utility of perturbation analysis as a tool for constraining networks in this and, in principle, any RD system.

scholarly journals Study on the Formation of Complex Chemical Waveforms by Different Computational Methods

Processes ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 393
Author(s):  
Jiali Ai ◽  
Chi Zhai ◽  
Wei Sun
Keyword(s):  
Reaction Kinetics ◽  
Spiral Wave ◽  
Reaction Diffusion ◽  
Local Concentration ◽  
Periodic Patterns ◽  
Concentration Difference ◽  
Complex Chemical ◽  
Mass Transfer Theory ◽  
Chemical Waves ◽  
Oregonator Model

Chemical wave is a special phenomenon that presents periodic patterns in space-time domain, and the Belousov–Zhabotinsky (B-Z) reaction is the first well-known reaction-diffusion system that exhibits organized patterns out of a homogeneous environment. In this paper, the B-Z reaction kinetics is described by the Oregonator model, and formation and evolution of chemical waves are simulated based on this model. Two different simulation methods, partial differential equations (PDEs) and cellular automata (CA) are implemented to simulate the formation of chemical waveform patterns, i.e., target wave and spiral wave on a two-dimensional plane. For the PDEs method, reaction caused changes of molecules at different location are considered, as well as diffusion driven by local concentration difference. Specifically, a PDE model of the B-Z reaction is first established based on the B-Z reaction kinetics and mass transfer theory, and it is solved by a nine-point finite difference (FD) method to simulate the formation of chemical waves. The CA method is based on system theory, and interaction relations with the cells nearest neighbors are mainly concerned. By comparing these two different simulation strategies, mechanisms that cause the formation of complex chemical waves are explored, which provides a reference for the subsequent research on complex systems.

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