Professor JOHN KING's Outputs (75)

Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption (2018)
Journal Article
Foster, J., Gysbers, P., King, J., & Pelinovsky, D. (2018). Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption. Nonlinearity, 31(10), 4621-4648. https://doi.org/10.1088/1361-6544/aad30b

Bifurcations of self-similar solutions for reversing interfaces are studied in the slow diffusion equation with strong absorption. The self-similar solutions bifurcate from the time-independent solutions for standing interfaces. We show that such bif... Read More about Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption.

Lie symmetries of nonlinear parabolic-elliptic systems and their application to a tumour growth model (2018)
Journal Article
Cherniha, R., Davydovych, V., & King, J. R. (2018). Lie symmetries of nonlinear parabolic-elliptic systems and their application to a tumour growth model. Symmetry, 10(5), Article 171. https://doi.org/10.3390/sym10050171

A generalisation of the Lie symmetry method is applied to classify a coupled system of reaction-diffusion equations wherein the nonlinearities involve arbitrary functions in the limit case in which one equation of the pair is quasi-steady but the oth... Read More about Lie symmetries of nonlinear parabolic-elliptic systems and their application to a tumour growth model.

Limit-cycle oscillatory coexpression of cross-inhibitory transcription factors: a model mechanism for lineage promiscuity (2018)
Journal Article
Bokes, P., & King, J. R. (in press). Limit-cycle oscillatory coexpression of cross-inhibitory transcription factors: a model mechanism for lineage promiscuity. Mathematical Medicine and Biology, https://doi.org/10.1093/imammb/dqy003

Lineage switches are genetic regulatory motifs that govern and maintain the commitment of a developing cell to a particular cell fate. A canonical example of a lineage switch is the pair of transcription factors PU.1 and GATA-1, of which the former i... Read More about Limit-cycle oscillatory coexpression of cross-inhibitory transcription factors: a model mechanism for lineage promiscuity.

Upscaling Diffusion Through First-Order Volumetric Sinks: A Homogenization of Bacterial Nutrient Uptake (2018)
Journal Article
Dalwadi, M. P., Wang, Y., King, J. R., & Minton, N. P. (2018). Upscaling Diffusion Through First-Order Volumetric Sinks: A Homogenization of Bacterial Nutrient Uptake. SIAM Journal on Applied Mathematics, 78(3), 1300-1329. https://doi.org/10.1137/17m1138625

In mathematical models that include nutrient delivery to bacteria, it is prohibitively expensive to include a pointwise nutrient uptake within small bacterial regions over bioreactor length-scales, and so such models often impose an effective uptake... Read More about Upscaling Diffusion Through First-Order Volumetric Sinks: A Homogenization of Bacterial Nutrient Uptake.

Finite indentation of highly curved elastic shells (2018)
Journal Article
Pearce, S. P., King, J. R., Steinbrecher, T., Leubner-Metzger, G., Everitt, N. M., & Holdsworth, M. J. (2018). Finite indentation of highly curved elastic shells. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474(2209), https://doi.org/10.1098/rspa.2017.0482

Experimentally measuring the elastic properties of thin biological surfaces is non-trivial, particularly when they are curved. One technique that may be used is the indentation of a thin sheet of material by a rigid indenter, whilst measuring the app... Read More about Finite indentation of highly curved elastic shells.

Applying asymptotic methods to synthetic biology: modelling the reaction kinetics of the mevalonate pathway (2017)
Journal Article
Dalwadi, M. P., Garavaglia, M., Webb, J. P., King, J. R., & Minton, N. P. (2018). Applying asymptotic methods to synthetic biology: modelling the reaction kinetics of the mevalonate pathway. Journal of Theoretical Biology, 439, https://doi.org/10.1016/j.jtbi.2017.11.022

The mevalonate pathway is normally found in eukaryotes, and allows for the production of isoprenoids, a useful class of organic compounds. This pathway has been successfully introduced to Escherichia coli, enabling a biosynthetic production route for... Read More about Applying asymptotic methods to synthetic biology: modelling the reaction kinetics of the mevalonate pathway.

New type I ancient compact solutions of the Yamabe flow (2017)
Journal Article
Daskalopoulos, P., del Pino, M., King, J., & Sesum, N. (2017). New type I ancient compact solutions of the Yamabe flow. Mathematical Research Letters, 24(6), 1667-1691. https://doi.org/10.4310/MRL.2017.v24.n6.a5

We construct new ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as t→−∞, to two self-similar complete non-compact solutions to the Yamabe flow moving in opposite directions. They are type I ancien... Read More about New type I ancient compact solutions of the Yamabe flow.

Multi-timescale analysis of a metabolic network in synthetic biology: a kinetic model for 3-hydroxypropionic acid production via beta-alanine (2017)
Journal Article
Dalwadi, M. P., King, J. R., & Minton, N. P. (2018). Multi-timescale analysis of a metabolic network in synthetic biology: a kinetic model for 3-hydroxypropionic acid production via beta-alanine. Journal of Mathematical Biology, 77(1), 165-199. https://doi.org/10.1007/s00285-017-1189-3

A biosustainable production route for 3-hydroxypropionic acid (3HP), an important platform chemical, would allow 3HP to be produced without using fossil fuels. We are interested in investigating a potential biochemical route to 3HP from pyruvate thro... Read More about Multi-timescale analysis of a metabolic network in synthetic biology: a kinetic model for 3-hydroxypropionic acid production via beta-alanine.

Stress-dependent local oxidation of silicon (2017)
Journal Article
Evans, J. D., & King, J. R. (2017). Stress-dependent local oxidation of silicon. SIAM Journal on Applied Mathematics, 77(6), 2012-2039. https://doi.org/10.1137/16M1060613

The two-dimensional isolation oxidation of silicon is considered for stress-dependent reaction and diffusion coefficients. The influence of such parameters is investigated numerically and asymptotically in the bird's beak problem and for curved geome... Read More about Stress-dependent local oxidation of silicon.

Root hydrotropism is controlled via a cortex-specific growth mechanism (2017)
Journal Article
Dietrich, D., Pang, L., Kobayashi, A., Fozard, J. A., Boudolf, V., Bhosale, R., Antoni, R., Nguyen, T., Hiratsuka, S., Fujii, N., Miyazawa, Y., Bae, T.-W., Wells, D. M., Owen, M. R., Band, L. R., Dyson, R. J., Jensen, O. E., King, J. R., Tracy, S. R., Sturrock, C. J., …Bennett, M. J. (2017). Root hydrotropism is controlled via a cortex-specific growth mechanism. Nature Plants, 3(6), Article 17057. https://doi.org/10.1038/nplants.2017.57

Plants can acclimate by using tropisms to link the direction of growth to environmental conditions. Hydrotropism allows roots to forage for water, a process known to depend on abscisic acid (ABA) but whose molecular and cellular basis remains unclear... Read More about Root hydrotropism is controlled via a cortex-specific growth mechanism.

Theoretical approaches to understanding root vascular patterning: a consensus between recent models (2016)
Journal Article
Mellor, N., Adibi, M., El-Showk, S., De Rybel, B., King, J., Mähönen, A. P., Weijers, D., & Bishopp, A. (in press). Theoretical approaches to understanding root vascular patterning: a consensus between recent models. Journal of Experimental Botany, https://doi.org/10.1093/jxb/erw410

The root vascular tissues provide an excellent system for studying organ patterning, as the specification of these tissues signals a transition from radial symmetry to bisymmetric patterns. The patterning process is controlled by the combined action... Read More about Theoretical approaches to understanding root vascular patterning: a consensus between recent models.

Biphasic regulation of the transcription factor ABORTED MICROSPORES (AMS) is essential for tapetum and pollen development in Arabidopsis (2016)
Journal Article
Ferguson, A., Pearce, S., Band, L. R., Yang, C., Ferjentsikova, I., King, J., Yuan, Z., Zhang, D., & Wilson, Z. A. (in press). Biphasic regulation of the transcription factor ABORTED MICROSPORES (AMS) is essential for tapetum and pollen development in Arabidopsis. New Phytologist, 213, https://doi.org/10.1111/nph.14200

Viable pollen is essential for plant reproduction and crop yield. Its production requires coordinated expression at specific stages during anther development, involving early meiosis-associated events and late pollen wall formation. The ABORTED MICRO... Read More about Biphasic regulation of the transcription factor ABORTED MICROSPORES (AMS) is essential for tapetum and pollen development in Arabidopsis.

Hybrid vertex-midline modelling of elongated plant organs (2016)
Journal Article
Fozard, J. A., Bennett, M. J., King, J. R., & Jensen, O. E. (2016). Hybrid vertex-midline modelling of elongated plant organs. Interface Focus, 6(5), Article 20160043. https://doi.org/10.1098/rsfs.2016.0043

We describe a method for the simulation of the growth of elongated plant organs, such as seedling roots. By combining a midline representation of the organ on a tissue scale and a vertex-based representation on the cell scale, we obtain a multiscale... Read More about Hybrid vertex-midline modelling of elongated plant organs.

Dynamic regulation of auxin oxidase and conjugating enzymes AtDAO1 and GH3 modulates auxin homeostasis (2016)
Journal Article
Mellor, N. L., Band, L. R., Pěnčík, A., Novak, O., Rashed, A., Holman, T., Wilson, M. H., Voss, U., Bishopp, A., King, J. R., Ljung, K., Bennett, M. J., & Owen, M. R. (2016). Dynamic regulation of auxin oxidase and conjugating enzymes AtDAO1 and GH3 modulates auxin homeostasis. Proceedings of the National Academy of Sciences, 113(39), 11022-11027. https://doi.org/10.1073/pnas.1604458113

Auxin is a key hormone regulating plant growth and development. We combine experiments and mathematical modeling to reveal how auxin levels are maintained via feedback regulation of genes encoding key metabolic enzymes. We describe how regulation of... Read More about Dynamic regulation of auxin oxidase and conjugating enzymes AtDAO1 and GH3 modulates auxin homeostasis.

The effects of insulin resistance on individual tissues: an application of a mathematical model of metabolism in humans (2016)
Journal Article
Pearson, T., Wattis, J. A., King, J., McDonald, I., & Mazzatti, D. (in press). The effects of insulin resistance on individual tissues: an application of a mathematical model of metabolism in humans. Bulletin of Mathematical Biology, 78(6), https://doi.org/10.1007/s11538-016-0181-1

Whilst the human body expends energy constantly, the human diet consists of a mix of carbohydrates and fats delivered in a discontinuous manner. To deal with this sporadic supply of energy, there are transport, storage and utilisation mechanisms, for... Read More about The effects of insulin resistance on individual tissues: an application of a mathematical model of metabolism in humans.

A multi-scale model of the interplay between cell signalling and hormone transport in specifying the root meristem of Arabidopsis thaliana (2016)
Journal Article
Muraro, D., Larrieu, A., Lucas, M., Chopard, J., Byrne, H. M., Godin, C., & King, J. R. (in press). A multi-scale model of the interplay between cell signalling and hormone transport in specifying the root meristem of Arabidopsis thaliana. Journal of Theoretical Biology, 404, https://doi.org/10.1016/j.jtbi.2016.04.036

The growth of the root of Arabidopsis thaliana is sustained by the meristem, a region of cell proliferation and differentiation which is located in the root apex and generates cells which move shootwards, expanding rapidly to cause root growth. The b... Read More about A multi-scale model of the interplay between cell signalling and hormone transport in specifying the root meristem of Arabidopsis thaliana.

Multicellular mathematical modelling of mesendoderm formation in amphibians (2016)
Journal Article
Brown, L., Middleton, A., King, J., & Loose, M. (2016). Multicellular mathematical modelling of mesendoderm formation in amphibians. Bulletin of Mathematical Biology, 78(3), 436-467. https://doi.org/10.1007/s11538-016-0150-8

The earliest cell fate decisions in a developing embryo are those associated with establishing the germ layers. The specification of the mesoderm and endoderm is of particular interest as the mesoderm is induced from the endoderm, potentially from an... Read More about Multicellular mathematical modelling of mesendoderm formation in amphibians.

Asymptotic analysis of a doubly nonlinear diffusion equation (2015)
Journal Article
King, J. R. (2016). Asymptotic analysis of a doubly nonlinear diffusion equation. Nonlinear Analysis: Theory, Methods and Applications, 138, https://doi.org/10.1016/j.na.2015.12.003

investigate the doubly nonlinear diffusion equation
∂u/∂t=1/n ∇.(u^m│∇u│^n-1) ∇u) and the same equation expressed in terms of a `pressure' variable. We classify various classes of compacted supported solutions, as well as finite-mass solutions that... Read More about Asymptotic analysis of a doubly nonlinear diffusion equation.

Pushed and pulled fronts in a discrete reaction-diffusion equation (2015)
Journal Article
King, J. R., & O'Dea, R. D. (2015). Pushed and pulled fronts in a discrete reaction-diffusion equation. Journal of Engineering Mathematics, https://doi.org/10.1007/s10665-015-9829-3

We consider the propagation of wave fronts connecting unstable and stable uniform solutions to a discrete reaction-diffusion equation on a one-dimensional integer lattice. The dependence of the wavespeed on the coupling strength µ between lattice poi... Read More about Pushed and pulled fronts in a discrete reaction-diffusion equation.

The Hele-Shaw injection problem for an extremely shear-thinning fluid (2015)
Journal Article
KING, J., & Richardson, G. (2015). The Hele-Shaw injection problem for an extremely shear-thinning fluid. European Journal of Applied Mathematics, 26(5), 563-594. https://doi.org/10.1017/S095679251500039X

We consider Hele-Shaw flows driven by injection of a highly shear-thinning power-law fluid (of exponent n) in the absence of surface tension. We formulate the problem in terms of the streamfunction ψ, which satisfies the p-Laplacian equation ∇·(|∇ψ|p... Read More about The Hele-Shaw injection problem for an extremely shear-thinning fluid.