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Article ; Online: Boundary Conditions Cause Different Generic Bifurcation Structures in Turing Systems.

Woolley, Thomas E

2022 Volume 84, Issue 9, Page(s) 101

Abstract: Turing's theory of morphogenesis is a generic mechanism to produce spatial patterning from near homogeneity. Although widely studied, we are still able to generate new results by returning to common dogmas. One such widely reported belief is that the ... ...

Abstract	Turing's theory of morphogenesis is a generic mechanism to produce spatial patterning from near homogeneity. Although widely studied, we are still able to generate new results by returning to common dogmas. One such widely reported belief is that the Turing bifurcation occurs through a pitchfork bifurcation, which is true under zero-flux boundary conditions. However, under fixed boundary conditions, the Turing bifurcation becomes generically transcritical. We derive these algebraic results through weakly nonlinear analysis and apply them to the Schnakenberg kinetics. We observe that the combination of kinetics and boundary conditions produce their own uncommon boundary complexities that we explore numerically. Overall, this work demonstrates that it is not enough to only consider parameter perturbations in a sensitivity analysis of a specific application. Variations in boundary conditions should also be considered.
MeSH term(s)	Kinetics ; Mathematical Concepts ; Models, Biological ; Morphogenesis
Language	English
Publishing date	2022-08-11
Publishing country	United States
Document type	Journal Article
ZDB-ID	184905-0
ISSN	1522-9602 ; 0007-4985 ; 0092-8240
ISSN (online)	1522-9602
ISSN	0007-4985 ; 0092-8240
DOI	10.1007/s11538-022-01055-x
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Article ; Online: Retinal Oxygenation With Conventional 100-ms Versus Short-Pulse Pan-Retinal Laser Photocoagulation.

Gallagher, Kevin / Ostler, Timothy / Woolley, Thomas E

Ophthalmic surgery, lasers & imaging retina

2024 Volume 55, Issue 1, Page(s) 40–45

Abstract: Background and objective: Conventional (100 ms) pan-retinal photocoagulation (PRP) laser burns are larger than short-pulse (10 ms to 20 ms) PRP burns. This study investigates the effect of PRP burns of different sizes on retinal oxygenation.: Method: ...

Abstract	Background and objective: Conventional (100 ms) pan-retinal photocoagulation (PRP) laser burns are larger than short-pulse (10 ms to 20 ms) PRP burns. This study investigates the effect of PRP burns of different sizes on retinal oxygenation. Method: A mathematical model using COMSOL Multiphysics 6 was used to create a three-dimensional abstraction of the coupled biology of the choroid, photoreceptor, and retinal tissues. Laser burn sizes were varied in the model, specifically considering burn diameters of 500 μm, 250 μm, and 125 μm, while keeping the total burn area constant. Results: Total increase in retinal oxygenation was the same for different burn sizes, but the oxygen distribution differed. Smaller burns resulted in a more even lateral oxygen distribution but with reduced penetration into the inner retina. Conclusions: Conventional and short-pulse PRP may affect retinal oxygenation differently, even when total burn area is the same. Further investigation into optimum burn size and pattern is required.
MeSH term(s)	Humans ; Retina/surgery ; Choroid ; Laser Coagulation ; Oxygen ; Radiation Injuries ; Lasers
Chemical Substances	Oxygen (S88TT14065)
Language	English
Publishing date	2024-01-01
Publishing country	United States
Document type	Journal Article
ZDB-ID	2701167-7
ISSN	2325-8179 ; 2325-8160
ISSN (online)	2325-8179
ISSN	2325-8160
DOI	10.3928/23258160-20231114-01
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Article ; Online: Bat Motion can be Described by Leap Frogging.

Henley, Lucy / Jones, Owen / Mathews, Fiona / Woolley, Thomas E

Bulletin of mathematical biology

2024 Volume 86, Issue 2, Page(s) 16

Abstract: We present models of bat motion derived from radio-tracking data collected over 14 nights. The data presents an initial dispersal period and a return to roost period. Although a simple diffusion model fits the initial dispersal motion we show that simple ...

Abstract	We present models of bat motion derived from radio-tracking data collected over 14 nights. The data presents an initial dispersal period and a return to roost period. Although a simple diffusion model fits the initial dispersal motion we show that simple convection cannot provide a description of the bats returning to their roost. By extending our model to include non-autonomous parameters, or a leap frogging form of motion, where bats on the exterior move back first, we find we are able to accurately capture the bat's motion. We discuss ways of distinguishing between the two movement descriptions and, finally, consider how the different motion descriptions would impact a bat's hunting strategy.
MeSH term(s)	Animals ; Chiroptera/physiology ; Mathematical Concepts ; Models, Biological ; Flight, Animal
Language	English
Publishing date	2024-01-10
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	184905-0
ISSN	1522-9602 ; 0007-4985 ; 0092-8240
ISSN (online)	1522-9602
ISSN	0007-4985 ; 0092-8240
DOI	10.1007/s11538-023-01233-5
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Article: A simple and fast method for estimating bat roost locations.

Henley, Lucy / Finch, Domhnall / Mathews, Fiona / Jones, Owen / Woolley, Thomas E

Royal Society open science

2024 Volume 11, Issue 4, Page(s) 231999

Abstract: Bats play a pivotal role in pest control, pollination and seed dispersal. Despite their ecological significance, locating bat roosts remains a challenging task for ecologists. Traditional field surveys are time-consuming, expensive and may disturb ... ...

Abstract	Bats play a pivotal role in pest control, pollination and seed dispersal. Despite their ecological significance, locating bat roosts remains a challenging task for ecologists. Traditional field surveys are time-consuming, expensive and may disturb sensitive bat populations. In this article, we combine data from static audio detectors with a bat movement model to facilitate the detection of bat roosts. Crucially, our technique not only provides a point prediction for the most likely location of a bat roost, but because of the algorithm's speed, it can be applied over an entire landscape, resulting in a likelihood map, which provides optimal searching regions. To illustrate the success of the algorithm and highlight limitations, we apply our technique to greater horseshoe bat (
Language	English
Publishing date	2024-04-24
Publishing country	England
Document type	Journal Article
ZDB-ID	2787755-3
ISSN	2054-5703
ISSN	2054-5703
DOI	10.1098/rsos.231999
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Article ; Online: Pattern production through a chiral chasing mechanism.

Woolley, Thomas E

Physical review. E

2017 Volume 96, Issue 3-1, Page(s) 32401

Abstract: Recent experiments on zebrafish pigmentation suggests that their typical black and white striped skin pattern is made up of a number of interacting chromatophore families. Specifically, two of these cell families have been shown to interact through a ... ...

Abstract	Recent experiments on zebrafish pigmentation suggests that their typical black and white striped skin pattern is made up of a number of interacting chromatophore families. Specifically, two of these cell families have been shown to interact through a nonlocal chasing mechanism, which has previously been modeled using integro-differential equations. We extend this framework to include the experimentally observed fact that the cells often exhibit chiral movement, in that the cells chase, and run away, at angles different to the line connecting their centers. This framework is simplified through the use of multiple small limits leading to a coupled set of partial differential equations which are amenable to Fourier analysis. This analysis results in the production of dispersion relations and necessary conditions for a patterning instability to occur. Beyond the theoretical development and the production of new pattern planiforms we are able to corroborate the experimental hypothesis that the global pigmentation patterns can be dependent on the chirality of the chromatophores.
Language	English
Publishing date	2017-09
Publishing country	United States
Document type	Journal Article
ZDB-ID	2844562-4
ISSN	2470-0053 ; 2470-0045
ISSN (online)	2470-0053
ISSN	2470-0045
DOI	10.1103/PhysRevE.96.032401
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Article ; Online: An Exploration of the Multiplicative Effect of "Other People" and Other Environmental Effects on Violence in the Night-Time Environment.

Moore, Simon C / Woolley, Thomas E / White, James

International journal of environmental research and public health

2022 Volume 19, Issue 24

Abstract: Background: The characteristics of night-time environments (NTEs) in which alcohol is consumed and that contribute to violence are poorly described. We explore competing explanations for violence in the NTE, with a particular focus on the number of ... ...

Abstract	Background: The characteristics of night-time environments (NTEs) in which alcohol is consumed and that contribute to violence are poorly described. We explore competing explanations for violence in the NTE, with a particular focus on the number of patrons and its association with assault-related visits to a hospital emergency department. Other environmental features including the weather and notable events were also considered. The primary aim was to stimulate debate around the causal mechanisms responsible for violence. Methods: Assault-related ED visits occurring between 8 pm and 4 am were recorded at the University Hospital of Wales, the single Emergency Department (ED) serving Cardiff, Wales, United Kingdom. Footfall was derived from the total number of unique MAC addresses recorded per hour collected from ten wireless fidelity monitoring tools located in the city centre. A narrative review of the literature concerning alcohol and violence informed exploratory analyses into the association between night-time footfall, sporting events, the weather, and other potential predictors of assault-related visits to the ED. We developed analytic methods from formal accounts of queueing. Results: International rugby matches at home, the weather (temperature), national holidays, the day of the week, and number of patrons in the NTE predicted assault-related injury (R Discussion: Assault-related visits to the ED have a non-linear association with the number of people socialising in the night-time environment and are further influenced by the weather and notable events. Opportunities for further research that might inform policy and interventions aimed at better managing NTEs are discussed.
MeSH term(s)	Humans ; Violence ; Crime Victims ; United Kingdom/epidemiology ; Wales/epidemiology ; Climate ; Emergency Service, Hospital
Language	English
Publishing date	2022-12-16
Publishing country	Switzerland
Document type	Review ; Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	2175195-X
ISSN	1660-4601 ; 1661-7827
ISSN (online)	1660-4601
ISSN	1661-7827
DOI	10.3390/ijerph192416963
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Article ; Online: Accounting for dimensional differences in stochastic domain invasion with applications to precancerous cell removal.

Woolley, Thomas E / Hill, William / Hogan, Catherine

Journal of theoretical biology

2022 Volume 541, Page(s) 111024

Abstract: We consider a specific form of domain invasion that is an abstraction of pancreatic tissue eliminating precancerous mutant cells through juxtacrine signalling. The model is explored discretely, continuously, stochastically and deterministically, ... ...

Abstract	We consider a specific form of domain invasion that is an abstraction of pancreatic tissue eliminating precancerous mutant cells through juxtacrine signalling. The model is explored discretely, continuously, stochastically and deterministically, highlighting unforeseen nonlinear dependencies on the dimension of the solution domain. Specifically, stochastically simulated populations invade with a dimension dependent wave speed that can be over twice as fast as their deterministic analogues. Although the wave speed can be analytically derived in the cases of small domains, the probabilistic state space grows exponentially and, thus, we use numeric simulation and curve fitting to predict limiting dynamics.
MeSH term(s)	Computer Simulation ; Humans ; Models, Biological ; Precancerous Conditions ; Signal Transduction ; Stochastic Processes
Language	English
Publishing date	2022-01-30
Publishing country	England
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	2972-5
ISSN	1095-8541 ; 0022-5193
ISSN (online)	1095-8541
ISSN	0022-5193
DOI	10.1016/j.jtbi.2022.111024
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Article: Covid-19 transmission modelling of students returning home from university.

Harper, Paul R / Moore, Joshua W / Woolley, Thomas E

Health systems (Basingstoke, England)

2021 Volume 10, Issue 1, Page(s) 31–40

Abstract: We provide an open-source model to estimate the number of secondary Covid-19 infections caused by potentially infectious students returning from university to private homes with other occupants. Using a Monte-Carlo method and data derived from UK sources, ...

Abstract	We provide an open-source model to estimate the number of secondary Covid-19 infections caused by potentially infectious students returning from university to private homes with other occupants. Using a Monte-Carlo method and data derived from UK sources, we predict that an infectious student would, on average, infect 0.94 other household members. Or, as a rule of thumb, each infected student would generate (just less than) one secondary within-household infection. The total number of secondary cases for all returning students is dependent on the virus prevalence within each student population at the time of their departure from campus back home. Although the proposed estimation method is general and robust, the results are sensitive to the input data. We provide Matlab code and a helpful online app (http://bit.ly/Secondary_infections_app) that can be used to estimate numbers of secondary infections based on local parameter values. This can be used worldwide to support policy making.
Language	English
Publishing date	2021-01-17
Publishing country	England
Document type	Journal Article
ZDB-ID	2669693-9
ISSN	2047-6973 ; 2047-6965
ISSN (online)	2047-6973
ISSN	2047-6965
DOI	10.1080/20476965.2020.1857214
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Article ; Online: Bespoke Turing Systems.

Woolley, Thomas E / Krause, Andrew L / Gaffney, Eamonn A

Bulletin of mathematical biology

2021 Volume 83, Issue 5, Page(s) 41

Abstract: Reaction-diffusion systems are an intensively studied form of partial differential equation, frequently used to produce spatially heterogeneous patterned states from homogeneous symmetry breaking via the Turing instability. Although there are many ... ...

Abstract	Reaction-diffusion systems are an intensively studied form of partial differential equation, frequently used to produce spatially heterogeneous patterned states from homogeneous symmetry breaking via the Turing instability. Although there are many prototypical "Turing systems" available, determining their parameters, functional forms, and general appropriateness for a given application is often difficult. Here, we consider the reverse problem. Namely, suppose we know the parameter region associated with the reaction kinetics in which patterning is required-we present a constructive framework for identifying systems that will exhibit the Turing instability within this region, whilst in addition often allowing selection of desired patterning features, such as spots, or stripes. In particular, we show how to build a system of two populations governed by polynomial morphogen kinetics such that the: patterning parameter domain (in any spatial dimension), morphogen phases (in any spatial dimension), and even type of resulting pattern (in up to two spatial dimensions) can all be determined. Finally, by employing spatial and temporal heterogeneity, we demonstrate that mixed mode patterns (spots, stripes, and complex prepatterns) are also possible, allowing one to build arbitrarily complicated patterning landscapes. Such a framework can be employed pedagogically, or in a variety of contemporary applications in designing synthetic chemical and biological patterning systems. We also discuss the implications that this freedom of design has on using reaction-diffusion systems in biological modelling and suggest that stronger constraints are needed when linking theory and experiment, as many simple patterns can be easily generated given freedom to choose reaction kinetics.
MeSH term(s)	Kinetics ; Models, Biological ; Systems Biology/methods
Language	English
Publishing date	2021-03-19
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	184905-0
ISSN	1522-9602 ; 0007-4985 ; 0092-8240
ISSN (online)	1522-9602
ISSN	0007-4985 ; 0092-8240
DOI	10.1007/s11538-021-00870-y
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Article ; Online: Gap junctions in Turing-type periodic feather pattern formation.

Tseng, Chun-Chih / Woolley, Thomas E / Jiang, Ting-Xin / Wu, Ping / Maini, Philip K / Widelitz, Randall B / Cheng-Ming, Chuong

PLoS biology

2024 Volume 22, Issue 5, Page(s) e3002636

Abstract: Periodic patterning requires coordinated cell-cell interactions at the tissue level. Turing showed, using mathematical modeling, how spatial patterns could arise from the reactions of a diffusive activator-inhibitor pair in an initially homogenous 2D ... ...

Abstract	Periodic patterning requires coordinated cell-cell interactions at the tissue level. Turing showed, using mathematical modeling, how spatial patterns could arise from the reactions of a diffusive activator-inhibitor pair in an initially homogenous 2D field. Most activators and inhibitors studied in biological systems are proteins, and the roles of cell-cell interaction, ions, bioelectricity, etc. are only now being identified. Gap junctions (GJs) mediate direct exchanges of ions or small molecules between cells, enabling rapid long-distance communications in a cell collective. They are therefore good candidates for propagating nonprotein-based patterning signals that may act according to the Turing principles. Here, we explore the possible roles of GJs in Turing-type patterning using feather pattern formation as a model. We found 7 of the 12 investigated GJ isoforms are highly dynamically expressed in the developing chicken skin. In ovo functional perturbations of the GJ isoform, connexin 30, by siRNA and the dominant-negative mutant applied before placode development led to disrupted primary feather bud formation. Interestingly, inhibition of gap junctional intercellular communication (GJIC) in the ex vivo skin explant culture allowed the sequential emergence of new feather buds at specific spatial locations relative to the existing primary buds. The results suggest that GJIC may facilitate the propagation of long-distance inhibitory signals. Thus, inhibition of GJs may stimulate Turing-type periodic feather pattern formation during chick skin development, and the removal of GJ activity would enable the emergence of new feather buds if the local environment were competent and the threshold to form buds was reached. We further propose Turing-based computational simulations that can predict the sequential appearance of these ectopic buds. Our models demonstrate how a Turing activator-inhibitor system can continue to generate patterns in the competent morphogenetic field when the level of intercellular communication at the tissue scale is modulated.
Language	English
Publishing date	2024-05-14
Publishing country	United States
Document type	Journal Article
ZDB-ID	2126776-5
ISSN	1545-7885 ; 1544-9173
ISSN (online)	1545-7885
ISSN	1544-9173
DOI	10.1371/journal.pbio.3002636
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