A Vertex Network Model of Arabidopsis Leaf Growth

doi:10.1007/s42967-023-00265-x

Abstract

Abstract: Biology provides many examples of complex systems whose properties allow organisms to develop in a highly reproducible, or robust, manner. One such system is the growth and development of flat leaves in Arabidopsis thaliana. This mechanistically challenging process results from multiple inputs including gene interactions, cellular geometry, growth rates, and coordinated cell divisions. To better understand how this complex genetic and cellular information controls leaf growth, we developed a mathematical model of flat leaf production. This two-dimensional model describes the gene interactions in a vertex network of cells which grow and divide according to physical forces and genetic information. Interestingly, the model predicts the presence of an unknown additional factor required for the formation of biologically realistic gene expression domains and iterative cell division. This two-dimensional model will form the basis for future studies into robustness of adaxial-abaxial patterning.

Key words: Robustness, Adaxial-abaxial patterning, Mathematical modeling, Gene regulatory networks (GRNs), Transcription factors, Small RNAs

Luke Andrejek, Janet Best, Ching-Shan Chou, Aman Husbands. A Vertex Network Model of Arabidopsis Leaf Growth[J]. Communications on Applied Mathematics and Computation, 2024, 6(1): 454-488.

TrendMD

References

[1] Andrejek, L., Chou, C.-S., Husbands, A.Y.:A robust mathematical model of adaxial-abaxial patterning. In silico Plants 3(1), diaa015 (2021)
[2] Center, O. S.:Ohio supercomputer center (1987)
[3] Chou, C.-S., Friedman, A.:Introduction to Mathematical Biology. Springer, New York (2016)
[4] Fox, S., Southam, P., Pantin, F., Kennaway, R., Robinson, S., Castorina, G., Sánchez-Corrales, Y.E., Sablowski, R., Chan, J., Grieneisen, V., et al.:Spatiotemporal coordination of cell division and growth during organ morphogenesis. PLoS Biol. 16(11), e2005952 (2018)
[5] Fukushima, K., Fujita, H., Yamaguchi, T., Kawaguchi, M., Tsukaya, H., Hasebe, M.:Oriented cell division shapes carnivorous pitcher leaves of Sarracenia purpurea. Nat. Commun. 6(1), 1-10 (2015)
[6] Galvan-Ampudia, C.S., Cerutti, G., Legrand, J., Brunoud, G., Martin-Arevalillo, R., Azais, R., Bayle, V., Moussu, S., Wenzl, C., Jaillais, Y., et al.:Temporal integration of auxin information for the regulation of patterning. Elife 9, e55832 (2020)
[7] Gelman, A., Gilks, W.R., Roberts, G.O.:Weak convergence and optimal scaling of random walk metropolis algorithms. Ann. Appl. Probab. 7(1), 110-120 (1997)
[8] Gonze, D., Abou-Jaoudé, W.:The Goodwin model:behind the Hill function. PloS One 8(8), e69573 (2013)
[9] Groenenboom, M.A.C., Marée, A.F.M., Hogeweg, P.:The RNA silencing pathway:the bits and pieces that matter. PLoS Comput. Biol. 1(2), e21 (2005)
[10] Hayakawa, Y., Tachikawa, M., Mochizuki, A.:Flat leaf formation realized by cell-division control and mutual recessive gene regulation. J. Theor. Biol. 404, 206-214 (2016)
[11] Husbands, A.Y., Benkovics, A.H., Nogueira, F.T., Lodha, M., Timmermans, M.C.:The asymmetric leaves complex employs multiple modes of regulation to affect adaxial-abaxial patterning and leaf complexity. Plant Cell 27(12), 3321-3335 (2015)
[12] Kierzkowski, D., Runions, A., Vuolo, F., Strauss, S., Lymbouridou, R., Routier-Kierzkowska, A.-L., Wilson-Sánchez, D., Jenke, H., Galinha, C., Mosca, G., et al.:A growth-based framework for leaf shape development and diversity. Cell 177(6), 1405-1418 (2019)
[13] LeVeque, R. J.:Finite Difference Methods for Ordinary and Partial Differential Equations:Steady-State and Time-Dependent Problems, Vol. 98. SIAM (2007)
[14] Merelo, P., Ram, H., Pia Caggiano, M., Ohno, C., Ott, F., Straub, D., Graeff, M., Cho, S.K., Yang, S.W., Wenkel, S., et al.:Regulation of MIR165/166 by class II and class III homeodomain leucine zipper proteins establishes leaf polarity. Proc. Natl. Acad. Sci. 113(42), 11973-11978 (2016)
[15] Murray, J.D.:Mathematical Biology:I. An Introduction, vol. 17. Springer Science & Business Media, Berlin (2007)
[16] Nagai, T., Honda, H.:A dynamic cell model for the formation of epithelial tissues. Philos. Mag. B 81(7), 699-719 (2001)
[17] Nakata, M., Matsumoto, N., Tsugeki, R., Rikirsch, E., Laux, T., Okada, K.:Roles of the middle domain-specific Wuschel-related homeobox genes in early development of leaves in Arabidopsis. Plant Cell 24(2), 519-535 (2012)
[18] Pekker, I., Alvarez, J.P., Eshed, Y.:Auxin response factors mediate Arabidopsis organ asymmetry via modulation of Kanadi activity. Plant Cell 17(11), 2899-2910 (2005)
[19] Poethig, R., Sussex, I.:The developmental morphology and growth dynamics of the tobacco leaf. Planta 165(2), 158-169 (1985)
[20] Scanlon, M.J., Schneeberger, R.G., Freeling, M.:The maize mutant narrow sheath fails to establish leaf margin identity in a meristematic domain. Development 122(6), 1683-1691 (1996)
[21] Skopelitis, D.S., Benkovics, A.H., Husbands, A.Y., Timmermans, M.C.:Boundary formation through a direct threshold-based readout of mobile small RNA gradients. Dev. Cell 43(3), 265-273 (2017)
[22] Smith, A.F., Roberts, G.O.:Bayesian computation via the Gibbs sampler and related Markov chain monte Carlo methods. J. Roy. Stat. Soc. B 55(1), 3-23 (1993)
[23] Sorenson, R.S., Deshotel, M.J., Johnson, K., Adler, F.R., Sieburth, L.E.:Arabidopsis mRNA decay landscape arises from specialized RNA decay substrates, decapping-mediated feedback, and redundancy. Proc. Natl. Acad. Sci. 115(7), E1485-E1494 (2018)
[24] Valdez-Taubas, J., Pelham, H.R.:Slow diffusion of proteins in the yeast plasma membrane allows polarity to be maintained by endocytic cycling. Curr. Biol. 13(18), 1636-1640 (2003)
[25] Van Ravenzwaaij, D., Cassey, P., Brown, S.D.:A simple introduction to Markov chain Monte-Carlo sampling. Psychonomic Bull. Rev. 25(1), 143-154 (2018)
[26] Volkening, A., Sandstede, B.:Iridophores as a source of robustness in zebrafish stripes and variability in danio patterns. Nat. Commun. 9(1), 1-14 (2018)
[27] Wu, G., Lin, W.-C., Huang, T., Poethig, R.S., Springer, P.S., Kerstetter, R.A.:Kanadi1 regulates adaxial-abaxial polarity in Arabidopsis by directly repressing the transcription of asymmetric leaves2. Proc. Natl. Acad. Sci. 105(42), 16392-16397 (2008)
[28] Zhang, L., Radtke, K., Zheng, L., Cai, A.Q., Schilling, T.F., Nie, Q.:Noise drives sharpening of gene expression boundaries in the zebrafish hindbrain. Mol. Syst. Biol. 8(1), 613 (2012)
[29] Zhang, Z., Runions, A., Mentink, R.A., Kierzkowski, D., Karady, M., Hashemi, B., Huijser, P., Strauss, S., Gan, X., Ljung, K., et al.:A WOX/auxin biosynthesis module controls growth to shape leaf form. Curr. Biol. 30(24), 4857-4868 (2020)
[30] Zhao, F., Du, F., Oliveri, H., Zhou, L., Ali, O., Chen, W., Feng, S., Wang, Q., Lü, S., Long, M., et al.:Microtubule-mediated wall anisotropy contributes to leaf blade flattening. Curr. Biol. 30(20), 3972-3985 (2020)
[31] Zhu, H., Hu, F., Wang, R., Zhou, X., Sze, S.-H., Liou, L.W., Barefoot, A., Dickman, M., Zhang, X.:Arabidopsis Argonaute10 specifically sequesters miR166/165 to regulate shoot apical meristem development. Cell 145(2), 242-256 (2011)