Developmental Tuning of Turing Patterning

Lead Research Organisation: University of Oxford
Department Name: Mathematical Institute


Our bodies arrange their own parts appropriately before we are born. We have only one of certain body parts (e.g. head, nose, spleen) and two of others (e.g. arm, eye, big toe) of, and these achieve their position through an equivalent of an embryo's Global Positioning System. However, still other structures, like hairs or nephrons of the kidney, are very numerous - too numerous to have a dedicated placing of each and every one of them. Instead, the body seems to use a simple "rule" to lay out these structures. This "rule" involves local interactions between cells which make sure that each follicle, nephron, or other structure, forms at a set distance from others of the same kind. Theoretical biologists have provided and proven general concepts that could underlie the operation of these "rules" and recent work by molecular biologists has substantiated and extended these theoretical ideas, identifying the specific genes and proteins that act as to set the "rule".

However, structures like hair follicles are not homogeneous across the body. For example, the eyebrows and scalp produce thicker hair types that mark these parts of the skin as being different from, for example, the forehead, which has very small, fine hairs. In this proposal we aim to understand how such distinctions in pattern, in this case of hair follicles serving as an example of other repeated structures, can be achieved. In essence, we will go up one level in organisation to understand how the size and spacing "rule" can be varied in different locations. This we will do by studying hair follicle formation on different parts of the mouse skin, with a focus on the various whiskers because of their distinctive pattern. Our project will be a combination of molecular and cell biology in analysing and manipulating the signals that pass between cells and mathematical simulations to interpret and guide the experimentation. Experiments will be done primarily on cultured skin samples, sparing use of intact animals. The intended outcome is to understand at both molecular and conceptual levels how the body can utilise a single pattern forming system by tuning in different regions to achieve a complex anatomy.

Technical Summary

The overall objective of this programme of work is to understand how a pattern forming system can be modulated to yield different outputs in different body regions. We will map signalling pathway activities by assessing pathway targets in different regions of the skin and determine growth parameters across the crucial stages of embryonic mouse hair follicle patterning. We will go on to modulate BMP, WNT and retinoic acid signalling on different parts of the body and assess pattern output, then determine the interactions between these pathways at the molecular level.

We will extract spatial placode distributions from experimental data, together with summary measures and statistics, such as the mean and variance of the inter-placode distance, i.e. the effective pattern wavelength. In turn this will allow comparison with detailed simulation and the estimation of the parameters required to match observation and theory, together with systematically classifying how close theory and experiment actually are, for hypothesis testing and also hypothesis generation and modelling development, for instance with regard to the understanding and modelling representation of the impact of retinoic acid. This can also be pursued on a regional basis to assess whether simple modulation can explain the spatial variation in different regions of the skin. Such comparisons will require systematic tools for data capture, which extract the evolution of the growing skin surface and capture the spatial distribution of placodes on this skin. Similarly, the systematic comparison of theory and observation will require the use of tools such as random forests and approximate Bayesian computation whilst the simulations will entail the solution of systems of reaction diffusion equations on evolving curved surfaces.

Planned Impact

This project will illuminate mechanisms of embryonic development and pattern formation, achieved by integrating tissue growth and intercellular signalling mechanisms within a rigorous mathematical framework.

Future practical implications arising from this work lie in understanding how specific signalling pathways are integrated to control appropriate organ development. Retinoic acid is already used as a dermatological treatment, for example in treatment of acne, and the EDA protein is in phase 2 clinical trial for treatment of the congenital condition hypohidrotic ectodermal dysplasia, caused by mutation of the gene encoding this protein (Edimer Pharmaceuticals). The interactions between these pathways and the others studied will help guide the practical use of these agents in therapies. The recent ability to target the EDA signalling pathway using newly developed reagents enables this pathway to be modulated, potentially including the emerging ability to use stimulators of this pathway in adult tissue regeneration of degenerated glandular structures, based on recent findings (e.g. Pharmacological activation of the EDA/EDAR signaling pathway restores salivary gland function following radiation-induced damage. Hill G, Headon D, Harris ZI, Huttner K, Limesand KH. PLoS One. 2014 9:e112840.). DH has funding from Edimer Pharmaceuticals to examine the potential of this pathway for therapeutic use in pre-clinical models. Growth of hair in adult skin is based on the action of the same signals as those operating in embryonic development to order the locations of hair primordia, thus industry impact in the area of identifying means to modulate hair growth through targetable molecular pathways is a later outcome from these studies. Such developments also have prospective impact in animal husbandry for agriculture, for instance enhancing sheep wool density to improve yield or reducing feather density to facilitate heat stress resistance in hotter climates.

In addition, the specific signalling interactions under study - those of the EDA, WNT, BMP and retinoic acid pathways - are relevant to the development of many vertebrate organs and will stimulate studies regarding the integration of these signals in a range of tissues. For instance, WNT signalling is a prime target for numerous cancer interventions, and thus its signalling, and how this might be quantitatively modelled, is of interest outside academia in the oncology research supporting the drug discovery programmes of large Pharmaceutical companies. One of us (EAG) has found parameter estimation a major challenge in work recently initiated with F. Hoffman LaRoche Ltd [via an industrially sponsored student at the pre-publication phase of her DPhil] exploring the modelling of a signalling pathway. Hence developing tools, which will be made freely available, for exploiting spatial data in parameter estimation, hypothesis testing and generation also has the prospect of impact not only in developmental biology but also in industrially focussed research. Furthermore, this prospective impact is not just scientific but also ethical, as it develops our ability to maximise the use of spatial data from animal experiments, noting that advances in imaging entail that spatial data is often readily available.

Finally, the general public has an interest in the beautiful patterns seen in nature and in the origins of these patterns. The public impact of this project upon the public will be enhanced by the 'real-world' nature of the model system studied; the distribution of hair of different types across the body. This model is easily appreciated by a lay audience and, combined with the striking images produced in studies of spatial patterning, this area is ideal for public engagement activities. In this regard the use of cultured skin tissues and computer simulation where appropriate in the project, rather than experimentation on intact animals, will aid public engagement and acceptance.


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Description The award is in its third year. We have been working with experimental collaborators, both virtually and in person, and have made progress in relating and explaining experimental observations, to the extent that we have potentially highly publishable results concerning spatially heterogeneities in patterning associated with hypothesised Turing systems. We are continuing to work closely with the experimental team to ascertain whether such results and the hypotheses underlying them can be verified in experiments. Here, the modelling serves to enable a control of the complexity, as well as rationalise and streamline the generation of hypothesis and the subsequent testing. In reaching the stage we have also advanced our understanding of Turing systems with spatial gradients. This has resulted in, currently, a theoretical manuscript that has been published and a combined theory and experimental manuscript that is being written. There has been industrial interest in our modelling experience in this research in the context of synthetic and programmable biology from the computational biology group at Microsoft Research, Cambridge, as detailed in the collaborator section.
Exploitation Route It is too early to say, though the increased understanding of how heterogeneity influences Turing's mechanism of self-organisation is likely to find wide impact in the diverse academic fields where the Turing mechanism is considered as, typically, the Turing mechanism refines pre-existing pattern rather than inducing an ab-initio symmetry breaking. Hence, this has the potential to impact a wide number of academic fields given the prospective ubiquity of Turing's mechanism but it is too early to say whether our findings will be developed and investigated by others. This is illustrated for example from the initiating collaboration with the Programmable Biology research group at Microsoft Research, Cambridge.
Sectors Agriculture, Food and Drink,Digital/Communication/Information Technologies (including Software)

Description MIcrosoft Research, Cambridge 
Organisation Microsoft Research
Department Microsoft Research Cambridge
Country United Kingdom 
Sector Private 
PI Contribution A collaboration with Microsoft Research, Cambridge, is in its very earliest stages concerning the synthetic biology of Turing patterning; we are providing insight and knowledge concerning how a Turing instability may be engineering in populations of cells, explicitly accounting for experimental details in Microsoft's research programme.
Collaborator Contribution The concept of a Turing instability in Synthetic Biology as part of a portfolio of research on programmable biology, which is a proof of principle study from many across the spectrum of biotechnology for health and industry.
Impact There are no outputs as yet, but a publication is planned shortly, and it is hoped to leverage funding for further study form Microsoft.
Start Year 2018
Title App for Public Awareness Events 
Description We developed a small app, that captures an image, e.g. of a face, and assesses how the grayscale intensity of the image is distorted by the diffusion and reaction processes that underlie Turing's mechanism. This will be used to explore some of the mathematical and biological ideas in a manner that requires no scientific background, to help with future public awareness activities that are planned. 
Type Of Technology Software 
Year Produced 2017 
Impact None (not yet) 
Title RD simulation 
Description We have developed some general methodologies for solving reaction diffusion models of Turing systems with diverse spatial heterogeneities, including spatial curvature. 
Type Of Technology Software 
Year Produced 2017 
Impact None 
Description Cardiff University 
Form Of Engagement Activity Participation in an open day or visit at my research institution
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Schools
Results and Impact An app concerning biological Reaction Diffusion was exhibited at Open Days for Cardiff University in 2017, 2018 together with details of the research. It has also featured in talks at the "Further Maths Support Programme", twice in 2018 and once so far in 2019.

The anticipated impact would be the encouragement and influence of school students and potential university students to engage in STEM subjects, including for their future university education.
Year(s) Of Engagement Activity 2017,2018,2019