Publications

For the most up to date list, please check out Google Scholar.

• J. Simmchen, D. Gordon, J. MacKenzie, I. Pagonabarraga, C.C. Roggartz, R.G. Endres, Z. Xiao, B. Friedrich, T. Qiu, K.J. Painter, R. Golestanian, C. Contini, M.C. Ucar, G. Yossifon, J.U. Sonner, W.J. Rappel, K. Wan, J. Armitage, R. Insall (2025+). Perspective on interdisciplinary approaches on Chemotaxis. Submitted.

• V. Freingruber, T. Lorenzi, M. Ptashnyk, K.J. Painter (2025+). Trait-structured chemotaxis: Exploring ligand-receptor dynamics and travelling wave properties in a Keller-Segel model. Link to arXiv version.

• T. Lorenzi, K.J. Painter, C. Villa (2025+). Phenotype structuring in collective cell migration: a tutorial of mathematical models and methods. Submitted. Link to arXiv version.

• S. Bernardi and K.J. Painter (2025+). The impact of different degrees of leadership on collective navigation in follower-leader systems. To appear in Bulletin of Mathematical Biology. Link to arXiv version.

• K.J. Painter, V, Giunta, J.R. Potts, S. Bernardi (2024). Variations in nonlocal interaction range lead to emergent chase-and-run in heterogeneous populations. Journal of the Royal Society Interface. 21, 20240409. Publisher version at https://doi.org/10.1098/rsif.2024.0409.  Open access at  Link to bioRxiv version.

• K.J. Painter (2024). Chemotaxis: a model phenomenon for making mathematical models. Educational piece appearing in European Communications in Mathematical and Theoretical Biology, Volume 27. Volume can be downloaded here.

• R.M. Crossley, K.J. Painter, T. Lorenzi, P.K. Maini, R.E. Baker (2024). Phenotypic switching mechanisms determine the structure of cell migration into extracellular matrix under the ‘go-or-grow’ hypothesis. Mathematical Biosciences, 109240. Open access at https://doi.org/10.1016/j.mbs.2024.109240. 

• T. Lorenzi, F.R. Macfarlane, K.J. Painter (2024). Derivation and travelling wave analysis of phenotype-structured haptotaxis models of cancer invasion. European Journal of Applied Mathematics. First view. Open access at https://doi.org/10.1017/S0956792524000056. Link to arXiv version.

• S.T. Johnston and K.J. Painter (2024). Avoidance, confusion or solitude? Modelling how noise pollution affects whale migration. Movement Ecology, 12, 17. Open access at https://doi.org/10.1186/s40462-024-00458-w. Link to bioRxiv version.

• J.R. Potts and K.J. Painter (2024). Distinguishing between long-transient and asymptotic states in a biological aggregation model. Bulletin of Mathematical Biology, 86, 28. Open access at https://doi.org/10.1007/s11538-023-01254-0. Link to arXiv version.

• V. Freingruber, K.J. Painter, M. Ptashnyk, L. Schumacher (2024). A biased random walk approach for modeling the collective chemotaxis of neural crest cells. Journal of Mathematical Biology, 88, 32. Open access at https://doi.org/10.1007/s00285-024-02047-2. Link to arXiv version.

• C. Fraga Delfino Kunz, A. Gerisch, J. Glover, D. Headon, K.J. Painter, F. Matthäus (2024). Novel aspects of pattern formation arise from coupling Turing reaction-diffusion and chemotaxis. Bulletin of Mathematical Biology, 86, 4. Open access at https://doi.org/10.1007/s11538-023-01225-5.

• T. Hillen, N. Loy, K.J. Painter, R. Thiessen (2024). Modelling microtube driven invasion of glioma. Journal of Mathematical Biology, 88, 4. Open access at https://doi.org/10.1007/s00285-023-02025-0. Link to bioRxiv version.

• K.J. Painter, T. Hillen, J.R. Potts (2024). Biological modelling with nonlocal advection diffusion equations. Mathematical Models and Methods in Applied Sciences (M3AS). Open access at https://doi.org/10.1142/S0218202524400025. Link to arXiv version.

• T.M. Hodgson, S.T. Johnston, M. Ottobre, K.J. Painter (2023). Intent matters: how flow and forms of information impact collective navigation. Journal of the Royal Society Interface, 20, 20230356. Open access at https://doi.org/10.1098/rsif.2023.0356. Link to bioRxiv version.

• B.D. Goddard, M. Ottobre, K.J. Painter, I. Souttar (2023). On the study of slow-fast dynamics, when the fast process has multiple invariant measures. Proceedings of the Royal Society A, 479, 20230322. https://doi.org/10.1098/rspa.2023.0322. Link to arXiv version.

• K.J. Painter and M. Winkler (2023). Phenotype switching in chemotaxis aggregation models controls the spontaneous emergence of large densities. SIAM Journal of Applied Mathematics, 83, 5. https://doi.org/10.1137/22M1539393.  Link to arXiv version.

• K.J. Painter, A. Gentile, S. Ferraris (2023). A stochastic cellular automaton model to describe the evolution of the snow-covered area across a high-elevation mountain catchment. Science of the Total Environment, 857, 159195. Open access at https://doi.org/10.1016/j.scitotenv.2022.159195

• P. Butta, B. Goddard, T. Hodgson, M. Ottobre and K.J. Painter (2022). Non-mean-field Vicsek-type models for collective behaviour. Mathematical Models and Methods in Applied Sciences (M3AS). 32, 2763-2816, https://doi.org/10.1142/S0218202522500646. Link to arXiv version.

• F.R. Macfarlane, T. Lorenzi, K.J. Painter (2022). The impact of phenotypic heterogeneity on chemotactic self-organisation. Bulletin of Mathematical Biology, 84, 143. Open access at https://doi.org/10.1007/s11538-022-01099-z.  Link to arXiv version.

• T. Lorenzi and K.J. Painter (2022). Trade-offs between chemotaxis and proliferation shape the phenotypic structuring of invading waves. International Journal of Non-Linear Mechanics, 139, 103885. https://doi.org/10.1016/j.ijnonlinmec.2021.103885.

• N. Loy, T. Hillen and K.J. Painter (2022). Direction-Dependent Turning Leads to Anisotropic Diffusion and Persistence. European Journal of Applied Mathematics, 33, 729-765. https://doi.org/10.1017/S0956792521000206 . Link to arXiv version.

• S. Bernardi, G. Estrada-Rodriguez, H. Gimperlein and K.J. Painter (2021). Macroscopic descriptions of follower-leader systems. Kinetic and Related Models, 14, 981-1002. https://doi.org/10.3934/krm.2021035. Link to arXiv version.

• K.J. Painter, M. Ptashnyk and D.J. Headon (2021). Systems for intricate patterning of the vertebrate anatomy. Philosophical Transactions of the Royal Society A, 379, 20200270. https://doi.org/10.1098/rsta.2020.0270.

• K.J. Painter (2021). The impact of rheotaxis and flow on the aggregation of organisms. Journal of the Royal Society Interface, 18, 20210582. https://doi.org/10.1098/rsif.2021.0582. Link to bioRxiv version.

• S.T. Johnston and K.J. Painter (2021). Modelling collective navigation via nonlocal communication. Journal of the Royal Society Interface, 18, 20210383. Open access at http://doi.org/10.1098/rsif.2021.0383. Link to bioRxiv version. 

• S. Bernardi, R. Eftimie and K.J. Painter (2021). Leadership through influence: what mechanisms allow leaders to influence a swarm. Bulletin of Mathematical Biology, 83, 69. Open access at https://doi.org/10.1007/s11538-021-00901-8. Link to arXiv version.

• J.R. Potts and K.J. Painter (2021). Stable steady-state solutions of some biological aggregation models. SIAM Journal on Applied Mathematics, 81(3), 1248-1263. https://doi.org/10.1137/20M1348066. Link to preprint version.

• 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. Open access at https://doi.org/10.1007/s00285-020-01536-4. Link to arXiv version 

• 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 version.

• 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. Open access at https://doi.org/10.1007/s00285-019-01421-9. 

• 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. Link to preprint.

• 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. Open access at https://doi.org/10.1371/journal.pbio.3000132. 

• 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.

• 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.

• 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. 

• 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. 

• 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 version .

• 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. https://doi.org/10.1007/978-3-319-96842-1_5. Link to preprint.

• 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 version. 

• 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. Link to preprint version.

• 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. Link to preprint version. 

• 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. 

• 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.

• 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. Open access at http://doi.org/10.1371/journal.pbio.2002117. 

• 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. Link to preprint version. 

• 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 version.

• 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. Link to preprint version. 

• 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. Open access at http://doi.org/10.1038/ncomms10288.  

• 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. Link to preprint version.  

• 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 version. 

• 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. Link to preprint version. 

• 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. Link to preprint version. 

• 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 version. 

• 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. Link to preprint version. 

• 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. 

• 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. 

• 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. 

• 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 Link to preprint version. 

• 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. Link to PDF.

• 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. Link to preprint. 

• C. Xue, H. Hwang, K.J. Painter, R. Erban (2011). Travelling waves in hyperbolic chemotaxis equations. Bulletin of Mathematical Biology, 73(8), 1695-1733. http://doi.org/10.1007/s11538-010-9586-4. Link to preprint.

• 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. Link to PDF.

• 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. Open access at http://doi.org/10.1371/journal.pbio.1001028. 

• 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. Open access at http://doi.org/10.1371/journal.pone.0015589. 

• 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. Open access at http://doi.org/10.1371/journal.pone.0013867. 

• 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. Link to PDF.

• 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. Link to PDF. 

• 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. Link to PDF.

• 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. Link to Preprint PDF.

• 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. Link to PDF. 

• 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. Link to PDF. 

• 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. Link to PDF. 

• 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. Link to PDF. 

• 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. Link to PDF. 

• 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. Link to PDF. 

• 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. Link to PDF. 

• 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. Link to PDF. 

• 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. Link to PDF. 

• 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. Link to PDF. 

• 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. Link to PDF. 

• 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. Link to PDF.

• 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. Link to PDF. 

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

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

• 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. Link to PDF. 

• 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. Link to PDF. 

• 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. Link to PDF. 

• 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. Link to PDF.

• 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. Open access at http://doi.org/10.1073/pnas.96.10.5549. Link to PDF. 

• 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. Link to PDF. 

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