Outputs (15)

Turing Instabilities are Not Enough to Ensure Pattern Formation (2024)
Journal Article
Krause, A. L., Gaffney, E. A., Jewell, T. J., Klika, V., & Walker, B. J. (2024). Turing Instabilities are Not Enough to Ensure Pattern Formation. Bulletin of Mathematical Biology, 86(2), Article 21. https://doi.org/10.1007/s11538-023-01250-4

Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing’s reaction–diffusion theory, which connects cellular signalling and transport with the d... Read More about Turing Instabilities are Not Enough to Ensure Pattern Formation.

Turing Pattern Formation in Reaction-Cross-Diffusion Systems with a Bilayer Geometry (2024)
Journal Article
Diez, A., Krause, A. L., Maini, P. K., Gaffney, E. A., & Seirin-Lee, S. (2024). Turing Pattern Formation in Reaction-Cross-Diffusion Systems with a Bilayer Geometry. Bulletin of Mathematical Biology, 86(2), Article 13. https://doi.org/10.1007/s11538-023-01237-1

Conditions for self-organisation via Turing’s mechanism in biological systems represented by reaction-diffusion or reaction-cross-diffusion models have been extensively studied. Nonetheless, the impact of tissue stratification in such systems is unde... Read More about Turing Pattern Formation in Reaction-Cross-Diffusion Systems with a Bilayer Geometry.

Patterning of nonlocal transport models in biology: The impact of spatial dimension (2023)
Journal Article
Jewell, T. J., Krause, A. L., Maini, P. K., & Gaffney, E. A. (2023). Patterning of nonlocal transport models in biology: The impact of spatial dimension. Mathematical Biosciences, 366, Article 109093. https://doi.org/10.1016/j.mbs.2023.109093

Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their awareness of other a... Read More about Patterning of nonlocal transport models in biology: The impact of spatial dimension.

VisualPDE: Rapid Interactive Simulations of Partial Differential Equations (2023)
Journal Article
Walker, B. J., Townsend, A. K., Chudasama, A. K., & Krause, A. L. (2023). VisualPDE: Rapid Interactive Simulations of Partial Differential Equations. Bulletin of Mathematical Biology, 85(11), Article 113. https://doi.org/10.1007/s11538-023-01218-4

Computing has revolutionised the study of complex nonlinear systems, both by allowing us to solve previously intractable models and through the ability to visualise solutions in different ways. Using ubiquitous computing infrastructure, we provide a... Read More about VisualPDE: Rapid Interactive Simulations of Partial Differential Equations.

Bat teeth illuminate the diversification of mammalian tooth classes (2023)
Journal Article
Sadier, A., Anthwal, N., Krause, A. L., Dessalles, R., Lake, M., Bentolila, L. A., …Sears, K. E. (2023). Bat teeth illuminate the diversification of mammalian tooth classes. Nature Communications, 14(1), Article 4687. https://doi.org/10.1038/s41467-023-40158-4

Tooth classes are an innovation that has contributed to the evolutionary success of mammals. However, our understanding of the mechanisms by which tooth classes diversified remain limited. We use the evolutionary radiation of noctilionoid bats to sho... Read More about Bat teeth illuminate the diversification of mammalian tooth classes.

Spatial heterogeneity localizes turing patterns in reaction-cross-diffusion systems (2023)
Journal Article
Gaffney, E. A., Krause, A. L., Maini, P. K., & Wang, C. (2023). Spatial heterogeneity localizes turing patterns in reaction-cross-diffusion systems. Discrete and Continuous Dynamical Systems - Series B, 28(12), 6092-6125. https://doi.org/10.3934/dcdsb.2023053

Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the presence of spatial heterogeneity in both transport and reaction term... Read More about Spatial heterogeneity localizes turing patterns in reaction-cross-diffusion systems.

The developmental basis of fingerprint pattern formation and variation (2023)
Journal Article
Glover, J. D., Sudderick, Z. R., Shih, B. B.-J., Batho-Samblas, C., Charlton, L., Krause, A. L., Anderson, C., Riddell, J., Balic, A., Li, J., Klika, V., Woolley, T. E., Gaffney, E. A., Corsinotti, A., Anderson, R. A., Johnston, L. J., Brown, S. J., Wang, S., Chen, Y., Crichton, M. L., & Headon, D. J. (2023). The developmental basis of fingerprint pattern formation and variation. Cell, 186(5), 940-956. https://doi.org/10.1016/j.cell.2023.01.015

Fingerprints are complex and individually unique patterns in the skin. Established prenatally, the molecular and cellular mechanisms that guide fingerprint ridge formation and their intricate arrangements are unknown. Here we show that fingerprint ri... Read More about The developmental basis of fingerprint pattern formation and variation.

Concentration-Dependent Domain Evolution in Reaction–Diffusion Systems (2023)
Journal Article
Krause, A. L., Gaffney, E. A., & Walker, B. J. (2023). Concentration-Dependent Domain Evolution in Reaction–Diffusion Systems. Bulletin of Mathematical Biology, 85(14), https://doi.org/10.1007/s11538-022-01115-2

Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating problems of pattern robustness and selection, in addition to more realistic modelling in... Read More about Concentration-Dependent Domain Evolution in Reaction–Diffusion Systems.

Fixed and Distributed Gene Expression Time Delays in Reaction-Diffusion Systems (2022)
Journal Article
Sargood, A., Gaffney, E. A., & Krause, A. L. (2022). Fixed and Distributed Gene Expression Time Delays in Reaction-Diffusion Systems. Bulletin of Mathematical Biology, 84(9), Article 98. https://doi.org/10.1007/s11538-022-01052-0

Time delays, modelling the process of intracellular gene expression, have been shown to have important impacts on the dynamics of pattern formation in reaction-diffusion systems. In particular, past work has shown that such time delays can shrink the... Read More about Fixed and Distributed Gene Expression Time Delays in Reaction-Diffusion Systems.

Turing and wave instabilities in hyperbolic reaction–diffusion systems: The role of second-order time derivatives and cross-diffusion terms on pattern formation (2022)
Journal Article
Ritchie, J. S., Krause, A. L., & Van Gorder, R. A. (2022). Turing and wave instabilities in hyperbolic reaction–diffusion systems: The role of second-order time derivatives and cross-diffusion terms on pattern formation. Annals of Physics, 444, Article 169033. https://doi.org/10.1016/j.aop.2022.169033

Hyperbolic reaction-diffusion equations have recently attracted attention both for their application to a variety of biological and chemical phenomena, and for their distinct features in terms of propagation speed and novel instabilities not present... Read More about Turing and wave instabilities in hyperbolic reaction–diffusion systems: The role of second-order time derivatives and cross-diffusion terms on pattern formation.