Publications

Publications

69. N. Loy, T. Hillen and K.J. Painter (2020+). Direction-Dependent Turning Leads to Anisotropic Diffusion and Persistence. Submitted for publication.

68. S. Bernardi, G. Estrada-Rodriguez, H. Gimperlein and K.J. Painter (2020+). Macroscopic descriptions of follower-leader systems. Submitted for publication.

67. S. Bernardi, R. Eftimie and K.J. Painter (2020+). Leadership through influence: what mechanisms allow leaders to influence a swarm. Submitted for publication.

66. J.R. Potts and K.J. Painter (2020+). Stable steady-state solutions of some biological aggregation models. Submitted for publication.

65. T. Hillen, K.J. Painter, M. Stolarska, C. Xue (2020). Nonlocal and local models for taxis in cell migration: a rigorous limit procedure. Journal of Mathematical Biology, 80, 275-281. https://doi.org/10.1007/s00285-020-01473-2.

64. M. Eckardt, K.J. Painter, C. Surulescu and A. Zhigun (2020). Nonlocal and local models for taxis in cell migration: a rigorous limit procedure. Journal of Mathematical Biology, 81, 1251-1298. https://doi.org/10.1007/s00285-020-01536-4. Link to arxiv version

63. L. Chen, K.J. Painter, C. Surulescu and A. Zhigun (2020). Mathematical models for cell migration: a nonlocal perspective. Philosophical Transactions of the Royal Society B: Biological Sciences, 375, 20190379. https://doi.org/10.1098/rstb.2019.0379.Link to Arxiv preprint. PDF to download.

62. A. Columbi, M. Scianna, K.J. Painter, L. Preziosi (2020). Modelling run and chase dynamics in neural crest/placode cell cultures. Journal of Mathematical Biology, 80, 423-456. Full text and supporting material at https://doi.org/10.1007/s00285-019-01421-9.

61. N. Bellomo, K.J. Painter, Y. Tao and M. Winkler (2019). Occurrence vs. absence of taxis-driven instabilities in a May-Nowak model for virus infection. SIAM Journal on Applied Mathematics 79(5), 1990-2010. https://doi.org/10.1137/19M1250261

60. W. Ho, L. Freem, D. Zhao, K.J. Painter, T.E. Woolley, E.A. Gaffney, M.J. McGrew, A.Tzika, M. Milinkovitch, P. Schneider, A. Drusko, F. Matthäus, J.L. Glover; K.L. Wells, J.A. Johansson, M.G. Davey, H.M. Sang, M. Clinton, D.J. Headon (2019). Feather Arrays are Patterned by Interacting Signalling and Cell Density Waves. PLoS Biology. 17(2), e3000132. Full text and supporting material at https://doi.org/10.1371/journal.pbio.3000132.

59. G. Estrada-Rodriguez, H. Gimperlein, K.J. Painter and J. Stocek (2019). Space-time fractional diffusion in cell movement models with delay. Mathematical Models and Methods in Applied Sciences 29(1), 65-88. http://doi.org/10.1142/S0218202519500039. Link to Arxiv preprint. PDF to download.

58. E. Moraki, K.J. Painter, R. Grima (2019). A stochastic model of corneal epithelium maintenance with applications to wound healing. Journal of Mathematical Biology, 78, 1245-1276. http://doi.org/10.1007/s00285-018-1308-9 Link to Biorxiv preprint. PDF to download.

57. K.J. Painter and A. Plochocka (2019). Multimodal navigation strategies for turtle homing. Ecological Modelling, 391, 40-52. http://doi.org/10.1016/j.ecolmodel.2018.10.025. Link to Biorxiv preprint. PDF to download.

56. S.T. Johnston and K.J. Painter (2019). The impact of short- and long-range perception on population movements. Journal of Theoretical Biology, 460, 227-242. http://doi.org/10.1016/j.jtbi.2018.10.031. Link to Biorxiv preprint. PDF to download.

55. K.J. Painter (2019). Mathematical models for chemotaxis and their applications in self-organisation phenomena. Journal of Theoretical Biology, 481, 162-182. http://doi.org/10.1016/j.jtbi.2018.06.019. Link to Arxiv preprint. PDF to download.

54. K.J. Painter and T. Hillen (2018). From random walks to fully anisotropic diffusion models for cell and animal movement. In Stolarska M., Tarfulea N. (eds) Cell Movement. Modeling and Simulation in Science, Engineering and Technology, pp.103-141. Birkhäuser, Cham.https://doi.org/10.1007/978-3-319-96842-1_5. PDF to download.

53. G. Estrada-Rodriguez, H. Gimperlein and K.J. Painter (2018). Fractional Patlak-Keller-Segel equations for chemotactic superdiffusion. SIAM Journal of Applied Mathematics, 78, 1155-1173. http://doi.org/10.1137/17M1142867. Link to Arxiv preprint. PDF to download.

52. T. Hillen, K.J. Painter and M. Winkler (2018). Global solvability and explicit bounds for a non-local adhesion model. European Journal of Applied Mathematics, 29, 645-684. http://doi.org/10.1017/S0956792517000328. PDF to download.

51. K.J. Painter, W. Ho and D.J. Headon (2018). A chemotaxis model of feather primordia pattern formation during avian development. Journal of Theoretical Biology 437, 225-238. http://doi.org/10.1016/j.jtbi.2017.10.026. PDF to download.

50. A. Buttenschoen, T. Hillen, A. Gerisch and K.J. Painter (2018). A space-jump derivation for non-local models of cell-cell adhesion and non-local chemotaxis. Journal of Mathematical Biology 76, 429-456. http://doi.org/10.1007/s00285-017-1144-3. Link to Biorxiv preprint. PDF to download.

49. I. Bica, T. Hillen and K.J. Painter (2017). Aggregation of biological particles under radial directional guidance. Journal of Theoretical Biology 427, 77-89. http://doi.org/10.1016/j.jtbi.2017.05.039. Link to Biorxiv preprint. PDF to download.

48. J. D. Glover, K. L. Wells, F. Matthäus, K.J. Painter, W. Ho, J. Riddell, J. A. Johansson, M. J. Ford, C. A. B. Jahoda, V. Klika, R. L. Mort, D. J. Headon (2017). Hierarchical patterning modes orchestrate hair follicle morphogenesis. PloS Biology, 15, e2002117. http://doi.org/10.1371/journal.pbio.2002117.

47. T. Hillen, K.J. Painter, A.C. Swan and A.D. Murtha (2017). Moments of von Mises and Fisher distributions and applications. Mathematical Biosciences and Engineering 14, 673-694. http://doi.org/10.3934/mbe.2017038. PDF to download.

46. A. Bianchi, K.J. Painter and J.A. Sherratt (2016). Spatio-temporal Models of Lymphangiogenesis in Wound Healing. Bulletin of Mathematical Biology 78, 1904-1941. http://doi.org/10.1007/s11538-016-0205-x. Link to Arxiv preprint. PDF to download.

45. G. Vasilopoulos and K.J. Painter (2016). Pattern formation in discrete cell tissues under long range filopodia-based direct cell to cell contact. Mathematical Biosciences 273, 1-15. http://doi.org/10.1016/j.mbs.2015.12.008. PDF to download.

44. R.L. Mort, R.J.H. Ross, K.J. Hainey, O.J. Harrison, M.A. Keighren, G. Landini, R.E. Baker, K.J. Painter, I.J. Jackson, C.A. Yates (2016). Reconciling diverse mammalian pigmentation patterns with a fundamental mathematical model. Nature Communications 7, 10288. http://doi.org/10.1038/ncomms10288.

43. K.J. Painter and T. Hillen (2015). Navigating the flow: individual and continuum models for homing in flowing environments. Journal of the Royal Society Interface 20150647. http://doi.org/10.1098/rsif.2015.0647. PDF to download.

42. A. Bianchi, K.J. Painter and J.A. Sherratt (2015). A mathematical model for lymphangiogenesis in normal and diabetic wounds. Journal of Theoretical Biology 383, 61-86. http://doi.org/10.1016/j.jtbi.2015.07.023. Link to Arxiv preprint. PDF to download.

41. K.J. Painter, J.M. Bloomfield, J.A. Sherratt and A. Gerisch (2015). A nonlocal model for contact attraction and repulsion in heterogeneous cell populations. Bulletin of Mathematical Biology 77, 1132-1165. http://doi.org/10.1007/s11538-015-0080-x. PDF to download.

40. K.J. Painter (2014). Multiscale models for movement in oriented environments and their application to hilltopping in butterflies. Theoretical Ecology 7, 53-75. http://doi.org/10.1007/s12080-013-0198-0. PDF to download.

39. B. Franz, C. Xue, K.J. Painter, R. Erban (2014). Travelling waves in hybrid chemotaxis models. Bulletin of Mathematical Biology 76, 377-400. http://doi.org/10.1007/s11538-013-9924-4. Link to Arxiv preprint. PDF to download.

38. T. Hillen, J. Zielinski and K.J. Painter (2013). Merging-emerging systems can describe spatio-temporal patterning in a chemotaxis model. Discrete & Continuous Dynamical Systems-Series B 18, 2513-2536. http://doi.org/10.3934/dcdsb.2013.18.2513. PDF to download.

37. T. Hillen, K.J. Painter and M. Winkler (2013). Anisotropic diffusion in oriented environments can lead to singularity formation. European Journal of Applied Mathematics 24, 371-413. http://doi.org/10.1017/S0956792512000447. PDF to download.

36. T. Hillen, K.J. Painter and M. Winkler (2013). Convergence of a cancer invasion model to a logistic chemotaxis model. Mathematical Models and Methods in Applied Sciences 23, 165-198. http://doi.org/10.1142/S0218202512500480. PDF to download.

35. T. Hillen and K.J. Painter (2013). Transport and anisotropic diffusion models for movement in oriented habitats. In Dispersal, individual movement and spatial ecology. Eds. M.A. Lewis, P.K. Maini, S.V. Petrovskii. 177-222. Lecture Notes in Mathematics Volume 2071, pp 177-222. http://doi.org/10.1007/978-3-642-35497-7_7. PDF to download.

34. K.J. Painter and T. Hillen (2013). Mathematical modelling of glioma growth: the use of diffusion tensor imaging (DTI) data to predict the anisotropic pathways of cancer invasion. Journal of Theoretical Biology 323, 25-39. http://doi.org/10.1016/j.jtbi.2013.01.014. PDF to download.

33. K.J. Painter, G.Hunt, K. Wells, J. Johanneson, D.J. Headon (2012). Towards an integrated experimental–theoretical approach for assessing the mechanistic basis of hair and feather morphogenesis. Interface Focus 2, 433-450. http://doi.org/10.1098/rsfs.2011.0122. Recommended by F1000 Prime. PDF to download.

32. K.J. Painter and T. Hillen (2011). Spatio-temporal chaos in a chemotaxis model. Physica D: Nonlinear Phenomena. 240, 363-375. http://doi.org/10.1016/j.physd.2010.09.011. PDF to download.

31. C. Xue, H. Hwang, K.J. Painter, R. Erban (2011). Travelling waves in hyperbolic chemotaxis equations. Bulletin of Mathematical Biology, 73(8), 1695-. http://doi.org/10.1007/s11538-010-9586-4. PDF to download.

30. J. Bloomfield, K.J. Painter and J.A. Sherratt (2011). How does cellular contact affect differentiation mediated pattern formation? Bulletin of Mathematical Biology. 73(7), 1529-1558. http://doi.org/10.1007/s11538-010-9578-4. PDF to download.

29. C. Mou, F. Pitel, D. Gourichon, F. Vignoles, A. Tzika, P. Tato, L. Yu, D.W. Burt, B. Bed'hom, M. Tixier-Boichard, K.J. Painter, D.J. Headon (2011). Cryptic Patterning of Avian Skin Confers a Developmental Facility for Loss of Neck Feathering. PLoS Biology 9(3), e1001028. Full text and supporting material at http://doi.org/10.1371/journal.pbio.1001028. PDF to download.

28. T. Saithong, K.J. Painter and A.J. Millar (2010). Consistent robustness analysis (CRA) identifies biologically relevant properties of regulatory network models. PLoS ONE. 5(12), e15589. Full text and supporting material at http://doi.org/10.1371/journal.pone.0015589. PDF to download.

27. T. Saithong, K.J. Painter and A.J. Millar (2010). The contributions of interlocking loops and extensive nonlinearity to the properties of circadian clock models. PLoS ONE. 5 (11), e13867. Full text and supporting material at http://doi.org/10.1371/journal.pone.0013867. PDF to download.

26. J. Bloomfield, J.A. Sherratt, K.J. Painter and G. Landini (2010). Cellular automata and integrodifferential equation models for cell proliferation in mosaic tissues. Journal of Royal Society Interface. 7, 1525-1535. http://doi.org/10.1098/rsif.2010.0071. PDF to download.

25. K.J. Painter, N. Armstrong and J.A. Sherratt (2010). The impact of adhesion on cellular invasion processes in cancer and development. Journal of Theoretical Biology. 264 (3), 1057-1067. http://doi.org/10.1016/j.jtbi.2010.03.033. PDF to download.

24. A. Gerisch and K.J. Painter (2010). Mathematical modelling of cell adhesion and its applications to developmental biology and cancer invasion. In Cell Mechanics: From Single Scale-Based Models to Multiscale Modeling. Editors: A. Chauviere and L. Preziosi. Chapter 12, 319-350. Book webpage. PDF to download.

23. H.G. Othmer, K. Painter , D. Umulis and C. Xue (2009). The intersection of theory and application in elucidating pattern formation in developmental biology. Mathematical Modelling of Natural Phenomena (MMNP). 4 (4), 3-83. http://doi.org/10.1051/mmnp/20094401. PDF to download.

22. D.J. Headon and K.J. Painter (2009). Stippling the skin: generation of anatomical periodicity by reaction-diffusion mechanisms. Mathematical Modelling of Natural Phenomena (MMNP). 4 (4), 84-102. http://doi.org/10.1051/mmnp/20094402. PDF to download.

21. K.J. Painter (2009). Continuous models for cell migration in tissues and applications to cell sorting via differential chemotaxis. Bulletin of Mathematical Biology. 71, 1117-1147. http://doi.org/10.1007/s11538-009-9396-8. PDF to download.

20. J.A. Sherratt, S.A. Gourley, N.J. Armstrong and K.J. Painter (2009). Boundedness of solutions of a nonlocal reaction-diffusion model for adhesion in cell aggregation and cancer invasion. European Journal of Applied Mathematics. 20, 123-144. http://doi.org/10.1017/S0956792508007742. PDF to download.

19. K.J. Painter (2009). Modelling cell migration strategies in the extracellular matrix. Journal of Mathematical Biology. 58, 511-543. http://doi.org/10.1007/s00285-008-0217-8. PDF to download.

18. N. Armstrong, K.J. Painter and J.A. Sherratt (2009). Adding adhesion to a chemical signalling model for somite formation. Bulletin of Mathematical Biology. 71, 1-24. http://doi.org/10.1007/s11538-008-9350-1. PDF to download.

17. T. Hillen and K.J. Painter (2009). A user's guide to PDE models for chemotaxis. Journal of Mathematical Biology. 58, 183-217. http://doi.org/10.1007/s00285-008-0201-3. Recommend by F1000 Prime. PDF to download.

16. R. Dillon, M. Owen and K.J. Painter (2008). A single-cell based model of multicellular growth using the immersed boundary method. In Moving Interface Problems and Applications in Fluid Dynamics. Editors: B. Cheong Khoo, Z. Li, P. Lin. Contemporary Mathematics, AMS. 1-16. PDF to download.

15. T. Hillen, K. Painter and C. Schmeiser (2007). Global existence for chemotaxis with finite sampling radius. Discrete and Continuous Dynamical Systems B. 7, 125-144. http://doi.org/10.3934/dcdsb.2007.7.125. PDF to download.

14. N. Armstrong, K.J. Painter and J. A. Sherratt (2006). A continuum approach to modelling cell-cell adhesion. Journal of Theoretical Biology, 243, 98-113. http://doi.org/10.1016/j.jtbi.2006.05.030. PDF to download.

13. S. Turner S, J.A. Sherratt, K.J. Painter and N. Savill (2004). From a discrete to a continuous model of biological cell movement. Physical Review E, 69, 021910. http://doi.org/10.1103/PhysRevE.69.021910. PDF to download.

12. D. Horstmann, K.J. Painter and H.G. Othmer (2004). Aggregation under local reinforcement: from lattice to continuum. European Journal of Applied Mathematics, 15, 545-576. http://doi.org/10.1017/S0956792504005571. PDF to download.

11. K.J. Painter and J. A. Sherratt (2003). Modelling the movement of interacting cell populations. Journal of Theoretical Biology, 225, 327-339. http://doi.org/10.1016/S0022-5193(03)00258-3. PDF to download.

10. K.J. Painter, D. Horstmann and H.G. Othmer (2003). Localization in lattice and continuum models of reinforced random walks. Applied Mathematical Letters, 16, 375-381. http://doi.org/10.1016/S0893-9659(03)80060-5. PDF to download.

9. K.J. Painter and T. Hillen (2002). Volume-filling and quorum-sensing in models for chemosensitive movement. Canadian Applied Mathematics Quarterly, 10, 501-544. PDF to download.

8. T. Hillen and K. Painter (2001). Global existence for a parabolic chemotaxis model with prevention of overcrowding. Advances in Applied Mathematics, 26, 280-301. http://doi.org/10.1006/aama.2001.0721. PDF to download.

7. S. Schnell, K.J. Painter , P.K. Maini and H.G. Othmer (2001). Spatiotemporal pattern formation in early development: a review of primitive streak formation and somitogenesis. In Mathematical Models for Biological Pattern Formation. Editors: P.K. Maini and H.G. Othmer. IMA Volumes in Mathematics and its Applications, 121, 11-38. Springer-Verlag, Berlin/Heidelberg. http://doi.org/10.1007/978-1-4613-0133-2_2. PDF to download.

6. K.J. Painter (2001). Modelling of pigment patterns in fish. In Mathematical Models for Biological Pattern Formation. Editors: P.K. Maini and H.G. Othmer. IMA Volumes in Mathematics and its Applications, 121, 59-82. Springer-Verlag, Berlin/Heidelberg. http://doi.org/10.1007/978-1-4613-0133-2_4. PDF to download.

5. K.J. Painter, P.K. Maini and H.G. Othmer (2000). Development and applications of a model for cellular response to multiple chemotactic cues. Journal of Mathematical Biology, 41, 285-314. http://doi.org/10.1007/s002850000035. PDF to download.

4. K.J. Painter, P.K. Maini and H.G. Othmer (2000). A chemotactic model for the advance and retreat of the primitive streak in avian development. Bulletin of Mathematical Biology, 62, 501-525. http://doi.org/10.1006/bulm.1999.0166. PDF to download.

3. K.J. Painter , H.G. Othmer and P.K. Maini (1999). Stripe formation in juvenile Pomacanthus via chemotactic response to a reaction-diffusion mechanism. Proceedings of National Academy Sciences USA, 96, 5549-5554. http://doi.org/10.1073/pnas.96.10.5549. PDF to download.

2. M.R. Myerscough, P.K. Maini and K.J. Painter (1998). Pattern formation in a generalized chemotactic model. Bulletin of Mathematical Biology, 60, 1-26. http://doi.org/10.1006/bulm.1997.0010. PDF to download.

1. P.K. Maini, K.J. Painter and H. Chau (1997). Spatial pattern formation in chemical and biological systems. Journal of Chemical Society Faraday Transactions, 93, 3601-3610. http://doi.org/10.1039/A702602A. PDF to download.

D. Phil Thesis

K.J. Painter (1997). Chemotaxis as a mechanism for Morphogenesis. D.Phil thesis, Brasenose College, University of Oxford. Abstract and PDF files for downloading.