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Modelling collective cell behaviour
1. | Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom, United Kingdom, United Kingdom |
References:
[1] |
K. Anguige and C. Schmeiser, A one-dimensional model of cell diffusion and aggregation, incorporating volume filling and cell-to-cell adhesion, J. Math. Biol., 58 (2009), 395-427.
doi: 10.1007/s00285-008-0197-8. |
[2] |
G. Ascolani, M. Badoual and C. Deroulers, Exclusion processes: Short-range correlations induced by adhesion and contact interactions, Phys. Rev. E, 87 (2013), 012702.
doi: 10.1103/PhysRevE.87.012702. |
[3] |
R. E. Baker and M. J. Simpson, Correcting mean-field approximations for birth-death-movement processes, Phys. Rev. E., 82 (2010), 041905, 12pp.
doi: 10.1103/PhysRevE.82.041905. |
[4] |
B. Bolker and S. W. Pacala, Using moment equations to understand stochastically driven spatial pattern formation in ecological systems, Theor. Pop. Biol., 52 (1997), 179-197.
doi: 10.1006/tpbi.1997.1331. |
[5] |
B. M. Bolker and S. W. Pacala, Spatial moment equations for plant competition: Understanding spatial strategies and the advantages of short dispersal, Theor. Pop. Biol., 153 (1999), 575-602.
doi: 10.1086/303199. |
[6] |
B. M. Bolker, S. W. Pacala and S. A. Levin, Moment methods for ecological processes in continuous space,, In The Geometry of Ecological Interactions: Simplifying Spatial Complexity, (): 338.
doi: 10.1017/CBO9780511525537.024. |
[7] |
B. M. Bolker, S. W. Pacala and C. Neuhauser, Spatial dynamics in model plant communities: What do we really know?, Am. Nat., 162 (2003), 135-148.
doi: 10.1086/376575. |
[8] |
U. Dieckmann and R. Law, Relaxation projections and the method of moments, Cambridge University Press, 21 (2000), 412-457. |
[9] |
R. Durrett and S. Levin, The importance of being discrete (and spatial), Theor. Pop. Biol., 46 (1994), 363-394.
doi: 10.1006/tpbi.1994.1032. |
[10] |
L. Dyson, P. K. Maini and R. E. Baker, Macroscopic limits of individual-based models for motile cell populations with volume exclusion, Phys. Rev. E, 86 (2012), 031903.
doi: 10.1103/PhysRevE.86.031903. |
[11] |
A. Fasano, M. A. Herrero and M. R. Rodrigo, Slow and fast invasion waves in a model of acid-mediated tumour growth, Math. Biosci., 220 (2009), 45-56.
doi: 10.1016/j.mbs.2009.04.001. |
[12] |
R. A. Gatenby and E. T. Gawlinski, A reaction-diffusion model of cancer invasion, Cancer Res., 56 (1996), 5745-5753. |
[13] |
F. Graner and J. A. Glazier, Simulation of biological cell sorting using a two-dimensional extended Potts model, Phys. Rev. Lett., 69 (1992), 2013-2016.
doi: 10.1103/PhysRevLett.69.2013. |
[14] |
S. T. Johnston, M. J. Simpson and R. E. Baker, Mean-field descriptions of collective migration with strong adhesion, Phys. Rev. E, 85 (2012), 051922.
doi: 10.1103/PhysRevE.85.051922. |
[15] |
M. J. Keeling, Correlation equations for endemic diseases: Externally imposed and internally generated heterogeneity, Proc. R. Soc. Lond. B, 266 (1999), 953-960.
doi: 10.1098/rspb.1999.0729. |
[16] |
M. J. Keeling, D. A. Rand and A. J. Morris, Correlation models for childhood epidemics, Proc. R. Soc. Lond. B, 264 (1997), 1149-1156.
doi: 10.1098/rspb.1997.0159. |
[17] |
J. G. Kirkwood, Statistical mechanics of fluid mixtures, J. Chem. Phys., 3 (1935), 300-314.
doi: 10.1063/1.1749657. |
[18] |
J. G. Kirkwood and E. M. Boggs, The radial distribution function in liquids, J. Chem. Phys., 10 (1942), 394-403.
doi: 10.1063/1.1723737. |
[19] |
R. Law, D. J. Murrell and U. Dieckmann, Population growth in space and time: Spatial logistic equations, Ecology, 84 (2003), 252-262. |
[20] |
M. A. Lewis and S. Pacala, Modeling and analysis of stochastic invasion processes, Theor. Pop. Biol., 41 (2000), 387-429.
doi: 10.1007/s002850000050. |
[21] |
P. M. Lushnikov, N. Chen and M. Alber, Macroscopic dynamics of biological cells interacting via chemotaxis and direct contact, Phys. Rev. E, 78 (2008), 061904.
doi: 10.1103/PhysRevE.78.061904. |
[22] |
J. Mai, V. N. Kuzovkov and W. von Niessen, A theoretical stochastic model for the $a + 1/2b_2\to0$ reaction, J. Chem. Phys., 98 (1993), 10017-10025. |
[23] |
J. Mai, V. N. Kuzovkov and W. von Niessen, A general stochastic model for the description of surface reaction systems, Physica A, 203 (1994), 298-315.
doi: 10.1016/0378-4371(94)90158-9. |
[24] |
D. C. Markham, M. J. Simpson and R. E. Baker, Simplified method for including spatial correlations in mean-field approximations, Phys. Rev. E, 87 (2013), 062702.
doi: 10.1103/PhysRevE.87.062702. |
[25] |
D. C. Markham, M. J. Simpson, P. K. Maini, E. A. Gaffney and R. E. Baker, Incorporating spatial correlations into multispecies mean-field models, Phys. Rev. E, 88 (2013), 052713.
doi: 10.1103/PhysRevE.88.052713. |
[26] |
J. B. McGillen, E. A. Gaffney, N. K. Martin and P. K. Maini, A general reaction-diffusion model of acidity in cancer invasion, J. Math. Biol., 68 (2014), 1199-1224.
doi: 10.1007/s00285-013-0665-7. |
[27] |
F. A. Meineke, C. S. Potten and M. Loeffler, Cell migration and organization in the intestinal crypt using a lattice-free model, Cell Prolif., 34 (2001), 253-266.
doi: 10.1046/j.0960-7722.2001.00216.x. |
[28] |
P. J. Murray, C. M. Edwards, M. J. Tindall and P. K. Maini, From a discrete to a continuum model of cell dynamics in one dimension, Phys. Rev. E, 80 (2009), 031912.
doi: 10.1103/PhysRevE.80.031912. |
[29] |
P. J. Murray, C. M. Edwards, M. J. Tindall and P. K. Maini, Classifying general nonlinear force laws in cell-based models via the continuum limit, Phys. Rev. E, 85 (2012), 021921.
doi: 10.1103/PhysRevE.85.021921. |
[30] |
D. J. Murrell, U. Dieckmann and R. Law, On moment closures for population dynamics in continuous space, J. Theor. Biol., 229 (2004), 421-432.
doi: 10.1016/j.jtbi.2004.04.013. |
[31] |
H. G. Othmer and A. Stevens, Aggregation, blowup, and collapse: The ABC's of taxis in reinforced random walks, SIAM J. Appl. Math., 57 (1997), 1044-1081.
doi: 10.1137/S0036139995288976. |
[32] |
K. J. Painter and T. Hillen, Volume-filling and quorum-sensing in models for chemosensitive movement, Canadian Appl. Math. Quarterly, 10 (2002), 501-543. |
[33] |
M. Raghib, N. A. Hill and U. Dieckmann, A multiscale maximum entropy moment closure for locally regulated space-time point process models of population dynamics, J. Math. Biol., 62 (2011), 605-653.
doi: 10.1007/s00285-010-0345-9. |
[34] |
K. J. Sharkey, Deterministic epidemic models on contact networks: Correlations and unbiological terms, Theor. Pop. Biol., 79 (2011), 115-129.
doi: 10.1016/j.tpb.2011.01.004. |
[35] |
K. J. Sharkey, C. Fernandez, K. L. Morgan, E. Peeler, M. Thrush, J. F. Turnbull and G. B. Bowers, Pair-level approximations to the spatio-temporal dynamics of epidemics on asymmetric contact networks, J. Math. Biol., 53 (2006), 61-85.
doi: 10.1007/s00285-006-0377-3. |
[36] |
M. J. Simpson and R. E. Baker, Corrected mean-field models for spatially dependent advection-diffusion-reaction phenomena, Phys. Rev. E, 83 (2011), 051922.
doi: 10.1103/PhysRevE.83.051922. |
[37] |
M. J. Simpson, B. J. Binder, P. Haridas, B. K. Wood, K. K. Treloar, D. L. S. McElwain and R. E. Baker, Experimental and modelling investigation of monolayer development with clustering, Bull. Math. Biol., 75 (2013), 871-889.
doi: 10.1007/s11538-013-9839-0. |
[38] |
O. Warburg and F. Dickens, The metabolism of tumors, Am. J. Med. Sci., 182 (1931), 123.
doi: 10.1097/00000441-193107000-00022. |
[39] |
W. R. Young, A. J. Roberts and G. Stuhne, Reproductive pair correlations and the clustering of organisms, Nature, 412 (2001), 328-331. |
show all references
References:
[1] |
K. Anguige and C. Schmeiser, A one-dimensional model of cell diffusion and aggregation, incorporating volume filling and cell-to-cell adhesion, J. Math. Biol., 58 (2009), 395-427.
doi: 10.1007/s00285-008-0197-8. |
[2] |
G. Ascolani, M. Badoual and C. Deroulers, Exclusion processes: Short-range correlations induced by adhesion and contact interactions, Phys. Rev. E, 87 (2013), 012702.
doi: 10.1103/PhysRevE.87.012702. |
[3] |
R. E. Baker and M. J. Simpson, Correcting mean-field approximations for birth-death-movement processes, Phys. Rev. E., 82 (2010), 041905, 12pp.
doi: 10.1103/PhysRevE.82.041905. |
[4] |
B. Bolker and S. W. Pacala, Using moment equations to understand stochastically driven spatial pattern formation in ecological systems, Theor. Pop. Biol., 52 (1997), 179-197.
doi: 10.1006/tpbi.1997.1331. |
[5] |
B. M. Bolker and S. W. Pacala, Spatial moment equations for plant competition: Understanding spatial strategies and the advantages of short dispersal, Theor. Pop. Biol., 153 (1999), 575-602.
doi: 10.1086/303199. |
[6] |
B. M. Bolker, S. W. Pacala and S. A. Levin, Moment methods for ecological processes in continuous space,, In The Geometry of Ecological Interactions: Simplifying Spatial Complexity, (): 338.
doi: 10.1017/CBO9780511525537.024. |
[7] |
B. M. Bolker, S. W. Pacala and C. Neuhauser, Spatial dynamics in model plant communities: What do we really know?, Am. Nat., 162 (2003), 135-148.
doi: 10.1086/376575. |
[8] |
U. Dieckmann and R. Law, Relaxation projections and the method of moments, Cambridge University Press, 21 (2000), 412-457. |
[9] |
R. Durrett and S. Levin, The importance of being discrete (and spatial), Theor. Pop. Biol., 46 (1994), 363-394.
doi: 10.1006/tpbi.1994.1032. |
[10] |
L. Dyson, P. K. Maini and R. E. Baker, Macroscopic limits of individual-based models for motile cell populations with volume exclusion, Phys. Rev. E, 86 (2012), 031903.
doi: 10.1103/PhysRevE.86.031903. |
[11] |
A. Fasano, M. A. Herrero and M. R. Rodrigo, Slow and fast invasion waves in a model of acid-mediated tumour growth, Math. Biosci., 220 (2009), 45-56.
doi: 10.1016/j.mbs.2009.04.001. |
[12] |
R. A. Gatenby and E. T. Gawlinski, A reaction-diffusion model of cancer invasion, Cancer Res., 56 (1996), 5745-5753. |
[13] |
F. Graner and J. A. Glazier, Simulation of biological cell sorting using a two-dimensional extended Potts model, Phys. Rev. Lett., 69 (1992), 2013-2016.
doi: 10.1103/PhysRevLett.69.2013. |
[14] |
S. T. Johnston, M. J. Simpson and R. E. Baker, Mean-field descriptions of collective migration with strong adhesion, Phys. Rev. E, 85 (2012), 051922.
doi: 10.1103/PhysRevE.85.051922. |
[15] |
M. J. Keeling, Correlation equations for endemic diseases: Externally imposed and internally generated heterogeneity, Proc. R. Soc. Lond. B, 266 (1999), 953-960.
doi: 10.1098/rspb.1999.0729. |
[16] |
M. J. Keeling, D. A. Rand and A. J. Morris, Correlation models for childhood epidemics, Proc. R. Soc. Lond. B, 264 (1997), 1149-1156.
doi: 10.1098/rspb.1997.0159. |
[17] |
J. G. Kirkwood, Statistical mechanics of fluid mixtures, J. Chem. Phys., 3 (1935), 300-314.
doi: 10.1063/1.1749657. |
[18] |
J. G. Kirkwood and E. M. Boggs, The radial distribution function in liquids, J. Chem. Phys., 10 (1942), 394-403.
doi: 10.1063/1.1723737. |
[19] |
R. Law, D. J. Murrell and U. Dieckmann, Population growth in space and time: Spatial logistic equations, Ecology, 84 (2003), 252-262. |
[20] |
M. A. Lewis and S. Pacala, Modeling and analysis of stochastic invasion processes, Theor. Pop. Biol., 41 (2000), 387-429.
doi: 10.1007/s002850000050. |
[21] |
P. M. Lushnikov, N. Chen and M. Alber, Macroscopic dynamics of biological cells interacting via chemotaxis and direct contact, Phys. Rev. E, 78 (2008), 061904.
doi: 10.1103/PhysRevE.78.061904. |
[22] |
J. Mai, V. N. Kuzovkov and W. von Niessen, A theoretical stochastic model for the $a + 1/2b_2\to0$ reaction, J. Chem. Phys., 98 (1993), 10017-10025. |
[23] |
J. Mai, V. N. Kuzovkov and W. von Niessen, A general stochastic model for the description of surface reaction systems, Physica A, 203 (1994), 298-315.
doi: 10.1016/0378-4371(94)90158-9. |
[24] |
D. C. Markham, M. J. Simpson and R. E. Baker, Simplified method for including spatial correlations in mean-field approximations, Phys. Rev. E, 87 (2013), 062702.
doi: 10.1103/PhysRevE.87.062702. |
[25] |
D. C. Markham, M. J. Simpson, P. K. Maini, E. A. Gaffney and R. E. Baker, Incorporating spatial correlations into multispecies mean-field models, Phys. Rev. E, 88 (2013), 052713.
doi: 10.1103/PhysRevE.88.052713. |
[26] |
J. B. McGillen, E. A. Gaffney, N. K. Martin and P. K. Maini, A general reaction-diffusion model of acidity in cancer invasion, J. Math. Biol., 68 (2014), 1199-1224.
doi: 10.1007/s00285-013-0665-7. |
[27] |
F. A. Meineke, C. S. Potten and M. Loeffler, Cell migration and organization in the intestinal crypt using a lattice-free model, Cell Prolif., 34 (2001), 253-266.
doi: 10.1046/j.0960-7722.2001.00216.x. |
[28] |
P. J. Murray, C. M. Edwards, M. J. Tindall and P. K. Maini, From a discrete to a continuum model of cell dynamics in one dimension, Phys. Rev. E, 80 (2009), 031912.
doi: 10.1103/PhysRevE.80.031912. |
[29] |
P. J. Murray, C. M. Edwards, M. J. Tindall and P. K. Maini, Classifying general nonlinear force laws in cell-based models via the continuum limit, Phys. Rev. E, 85 (2012), 021921.
doi: 10.1103/PhysRevE.85.021921. |
[30] |
D. J. Murrell, U. Dieckmann and R. Law, On moment closures for population dynamics in continuous space, J. Theor. Biol., 229 (2004), 421-432.
doi: 10.1016/j.jtbi.2004.04.013. |
[31] |
H. G. Othmer and A. Stevens, Aggregation, blowup, and collapse: The ABC's of taxis in reinforced random walks, SIAM J. Appl. Math., 57 (1997), 1044-1081.
doi: 10.1137/S0036139995288976. |
[32] |
K. J. Painter and T. Hillen, Volume-filling and quorum-sensing in models for chemosensitive movement, Canadian Appl. Math. Quarterly, 10 (2002), 501-543. |
[33] |
M. Raghib, N. A. Hill and U. Dieckmann, A multiscale maximum entropy moment closure for locally regulated space-time point process models of population dynamics, J. Math. Biol., 62 (2011), 605-653.
doi: 10.1007/s00285-010-0345-9. |
[34] |
K. J. Sharkey, Deterministic epidemic models on contact networks: Correlations and unbiological terms, Theor. Pop. Biol., 79 (2011), 115-129.
doi: 10.1016/j.tpb.2011.01.004. |
[35] |
K. J. Sharkey, C. Fernandez, K. L. Morgan, E. Peeler, M. Thrush, J. F. Turnbull and G. B. Bowers, Pair-level approximations to the spatio-temporal dynamics of epidemics on asymmetric contact networks, J. Math. Biol., 53 (2006), 61-85.
doi: 10.1007/s00285-006-0377-3. |
[36] |
M. J. Simpson and R. E. Baker, Corrected mean-field models for spatially dependent advection-diffusion-reaction phenomena, Phys. Rev. E, 83 (2011), 051922.
doi: 10.1103/PhysRevE.83.051922. |
[37] |
M. J. Simpson, B. J. Binder, P. Haridas, B. K. Wood, K. K. Treloar, D. L. S. McElwain and R. E. Baker, Experimental and modelling investigation of monolayer development with clustering, Bull. Math. Biol., 75 (2013), 871-889.
doi: 10.1007/s11538-013-9839-0. |
[38] |
O. Warburg and F. Dickens, The metabolism of tumors, Am. J. Med. Sci., 182 (1931), 123.
doi: 10.1097/00000441-193107000-00022. |
[39] |
W. R. Young, A. J. Roberts and G. Stuhne, Reproductive pair correlations and the clustering of organisms, Nature, 412 (2001), 328-331. |
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