A purely mechanical model with asymmetric features for early morphogenesis of rod-shaped bacteria micro-colony

Marie Doumic; Sophie Hecht; Diane Peurichard; Marie Doumic; Sophie Hecht; Diane Peurichard

doi:10.3934/mbe.2020356

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 6873-6908. doi: 10.3934/mbe.2020356

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A purely mechanical model with asymmetric features for early morphogenesis of rod-shaped bacteria micro-colony

Sorbonne Université, Inria, Université Paris-Diderot, CNRS, Laboratoire Jacques-Louis Lions, F-75005 Paris, France

Received: 11 June 2020 Accepted: 13 September 2020 Published: 12 October 2020

To model the morphogenesis of rod-shaped bacterial micro-colony, several individual-based models have been proposed in the biophysical literature. When studying the shape of micro-colonies, most models present interaction forces such as attraction or filial link. In this article, we propose a model where the bacteria interact only through non-overlapping constraints. We consider the asymmetry of the bacteria, and its influence on the friction with the substrate. Besides, we consider asymmetry in the mass distribution of the bacteria along their length. These two new modelling assumptions allow us to retrieve mechanical behaviours of micro-colony growth without the need of interaction such as attraction. We compare our model to various sets of experiments, discuss our results, and propose several quantifiers to compare model to data in a systematic way.
- micro-colony morphogenesis,
- rod-shaped bacteria,
- individual-based model,
- asymmetric friction
Citation: Marie Doumic, Sophie Hecht, Diane Peurichard. A purely mechanical model with asymmetric features for early morphogenesis of rod-shaped bacteria micro-colony[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 6873-6908. doi: 10.3934/mbe.2020356

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Abstract

To model the morphogenesis of rod-shaped bacterial micro-colony, several individual-based models have been proposed in the biophysical literature. When studying the shape of micro-colonies, most models present interaction forces such as attraction or filial link. In this article, we propose a model where the bacteria interact only through non-overlapping constraints. We consider the asymmetry of the bacteria, and its influence on the friction with the substrate. Besides, we consider asymmetry in the mass distribution of the bacteria along their length. These two new modelling assumptions allow us to retrieve mechanical behaviours of micro-colony growth without the need of interaction such as attraction. We compare our model to various sets of experiments, discuss our results, and propose several quantifiers to compare model to data in a systematic way.

References

[1]	M. C. Duvernoy, T. Mora, M. Ardré, V. Croquette, D. Bensimon, C. E. A. Quilliet, Asymmetric adhesion of rod-shaped bacteria controls microcolony morphogenesis, Nat. Commun., 9 (2018), 1120.
[2]	P. Ghosh, J. Mondal, E. Ben-Jacob, H. Levine, Mechanically-driven phase separation in a growing bacterial colony, PNAS, 112 (2015), E2166.
[3]	Z. You, D. J. G. Pearce, A. Sengupta, L. Giomi, Geometry and mechanics of microdomains in growing bacterial colonies, Phys. Rev. X, 8 (2018), 031065.
[4]	D. Boyer, W. Mather, O. Mondragón-Palomino, S. Orozco-Fuentes, T. Danino, J. Hasty, et al., Buckling instability in ordered bacterial colonies, Phys. Biol., 8 (2011), 026008.
[5]	D. Volfson, S. Cookson, J. Hasty, L. S. Tsimring, Biomechanical ordering of dense cell populations, PNAS, 105 (2008), 15346-15351.
[6]	H. Jönsson, A. Levchenko, An explicit spatial model of yeast microcolony growth, MMS, 3 (2005), 346-361.
[7]	M. A. A. Grant, B. Wacław, R. J. Allen, P. Cicuta, The role of mechanical forces in the planarto-bulk transition in growing escherichia coli microcolonies, J. R. Soc. Interface, 11 (2014), 20140400.
[8]	T. Storck, C. Picioreanu, B. Virdis, D. J. Batstone, Variable cell morphology approach for individual-based modeling of microbial communities, Biophys. J., 106 (2014), 2037-2048.
[9]	H. Cho, H. J?nsson, K. Campbell, P. Melke, J. W. Williams, B. Jedynak, et al., Self-organization in high-density bacterial colonies: Efficient crowd control, PLoS Biol., 5 (2007), e302.
[10]	D. Dell'Arciprete, M. L. Blow, A. T. Brown, F. D. C. Farrell, J. S. Lintuvuori, A. F. McVey, et al., A growing bacterial colony in two dimensions as an active nematic, Nat. Commun., 9 (2018), 4190.
[11]	A. Doostmohammadi, M. F. Adamer, S. P. Thampi, J. M. Yeomans, Stabilization of active matter by flow-vortex lattices and defect ordering, Nat. Commun., 7 (2016), 10557.
[12]	G. Ariel, A. Shklarsh, O. Kalisman, C. Ingham, E. Ben-Jacob, From organized internal traffic to collective navigation of bacterial swarms, New J. Phys., 15 (2013), 125019.
[13]	S. Park, P. M. Wolanin, E. A. Yuzbashyan, H. Lin, N. C. Darnton, J. B. Stock, et al., Influence of topology on bacterial social interaction, PNAS, 100 (2003), 13910.
[14]	E. B. Jacob, I. Becker, Y. Shapira, H. Levine, Bacterial linguistic communication and social intelligence, Trends Microbiol., 12 (2004), 366-372.
[15]	L. Giomi, N. Hawley-Weld, L. Mahadevan, Swarming, swirling and stasis in sequestered bristlebots, Proc. R. Soc. A, 469 (2013), 20120637.
[16]	E. J. Stewart, R. Madden, G. Paul, F. Taddei, Aging and death in an organism that reproduces by morphologically symmetric division, PLoS Biol., 3 (2005), e45.
[17]	J. A. Shapiro, C. Hsu, Escherichia coli k-12 cell-cell interactions seen by time-lapse video, J. Bacteriol. Res., 171 (1989), 5963-5974.
[18]	R. Acemel, F. Govantes, A. Cuetos, Computer simulation study of early bacterial biofilm development, Sci. Rep., 8 (2018), 5340.
[19]	P. T. Su, C. T. Liao, J. R. Roan, S. H. Wang, A. Chiou, W. J. Syu, Bacterial colony from twodimensional division to three-dimensional development, PLoS One, 7 (2012), e48098.
[20]	L. Hall-Stoodley, J. W. Costerton, P. Stoodley, Bacterial biofilms: from the natural environment to infectious diseases, Nat. Rev. Microbiol., 2 (2004), 95-108.
[21]	T. Shaw, M. Winston, C. J. Rupp, I. Klapper, P. Stoodley, Commonality of elastic relaxation times in biofilms, Phys. Rev. Lett., 93 (2004), 098102.
[22]	P. T. Su, P. W. Yen, S. H. Wang, C. H. Lin, A. Chiou, W. J. Syu, Factors affecting daughter cells' arrangement during the early bacterial divisions, PLoS One, 5 (2010), e9147.
[23]	F. D. C. Farrell, O. Hallatschek, D. Marenduzzo, B. Waclaw, Mechanically driven growth of quasi-two-dimensional microbial colonies, Phys. Rev. Lett., 111 (2013), 168101.
[24]	M. R. Warren, H. Sun, Y. Yan, J. Cremer, B. Li, T. Hwa, Spatiotemporal establishment of dense bacterial colonies growing on hard agar, ELife, 8 (2019), e41093.
[25]	P. Wang, L. Robert, J. Pelletier, W. L. Dang, F. Taddei, A. Wright, et al., Robust growth of escherichia coli, Curr. Biol., 20 (2010), 1099-1103.
[26]	B. Delyon, B. de Saporta, N. Krell, L. Robert, Investigation of asymmetry in E. coli growth rate, CSBIGS, 7 (2018), 1-13.
[27]	F. D. Farrell, M. Gralka, O. Hallatschek, B. Waclaw, Mechanical interactions in bacterial colonies and the surfing probability of beneficial mutations, J. R. Soc. Interface, 14 (2017), 20170073.
[28]	R. van Damme, J. Rodenburg, R. van Roij, M. Dijkstra, Interparticle torques suppress motilityinduced phase separation for rodlike particles, J. Chem. Phys., 150 (2019), 164501.
[29]	M. S. Kumar, P. Philominathan, The physics of flagellar motion of E. coli during chemotaxis, Biophys. Rev., 2 (2010), 13-20.
[30]	J. Shäfer, S. Dippel, D. E. Wolf, Force schemes in simulations of granular materials, J. Phys., 6 (1996), 5-20.
[31]	L. Robert, M. Hoffmann, N. Krell, S. Aymerich, J. Robert, M. Doumic, Division in Escherichia coli is triggered by a size-sensing rather than a timing mechanism, BMC Biol., 12 (2014), 17.
[32]	A. Amir, Cell size regulation in bacteria, Phys. Rev. Lett., 112 (2014), 20810.
[33]	S. Taheri-Araghi, S. Bradde, J. T. Sauls, N. S. Hill, P. A. Levin, J. Paulsson, et al., Cell-size control and homeostasis in bacteria, Curr. Biol., 25 (2015), 385-391.
[34]	J. T. Sauls, D. Li, S. Jun, Adder and a coarse-grained approach to cell size homeostasis in bacteria, Curr. Opin. Cell Biol., 38 (2016), 38-44.
[35]	G. F. Webb, Nonlinear Age-Dependent Population Dynamics in L1, Rocky Mountain Mathematics Consortium, 1983.
[36]	J. A. J. Metz, O. Diekmann, The Dynamics of Physiologically Structured Populations, SpringerVerlag, Berlin, 1986.
[37]	M. C. Duvernoy, Growth Mechanics of a Bacterial Microcolony, Université Grenoble Alpes, 2015.
[38]	M. Hoffmann, A. Olivier, Nonparametric estimation of the division rate of an age dependent branching process, Stoch. Process. Their Appl., 126 (2016), 1433-1471.
[39]	M. Doumic, M. Hoffmann, N. Krell, L. Robert, Statistical estimation of a growth-fragmentation model observed on a genealogical tree, Bernoulli, 21 (2015), 1760-1799.
[40]	P. Gabriel, H. Martin, Steady distribution of the incremental model for bacteria proliferation, Netw. Heterog. Media, 14 (2019), 149-171.
[41]	B. Perthame, Transport Equations in Biology, Frontiers in Mathematics, Birkh?user Verlag, Basel, 2007.
[42]	A. Olivier, How does variability in cells aging and growth rates influence the malthus parameter?, Kinet. Relat. Models, 10 (2017), 481-512.
[43]	M. Doumic, M. Hoffmann, P. Reynaud, V. Rivoirard, Nonparametric estimation of the division rate of a size-structured population, SIAM J. Numer. Anal., 50 (2012), 925-950.
[44]	C. Lacour, P. Massart, V. Rivoirard, Estimator selection: A new method with applications to kernel density estimation, Sankhya Ser A., 79 (2017), 298-335.
[45]	P. Van Liedekerke, M. M. Palm, N. Jagiella, D. Drasdo, Simulating tissue mechanics with agentbased models: concepts, perspectives and some novel results, Comp. Part. Mech., 2 (2015), 401–444.

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