Our research uses mathematical and computer simulation techniques to investigate questions in plant development. Working in close collaboration with experimental biologists, we develop cellular-level simulation models of hormone signaling and patterning in plant tissue. These models involve a biochemical aspect, genes, proteins, hormones, combined with growing, changing geometry as cells divide and tissues grow. We are interested in the interaction between these two processes. How genes control physical properties of cells resulting in growth, and how this resulting change in geometry and forces feeds back on signaling and gene regulation. With this in mind, we are researching methods to quantify physical properties in plant tissues, to facilitate the construction of biophysically-based simulation models of plant growth.

Our work is inter-disciplinary in nature, and we also aim to provide accessible courses on plant modeling designed for both biologists and mathematicians.

Inhibition model of phyllotaxis

In 1868 Hofmeister observed that new plant organs appear to form as far as possible from previous ones. A simulation model based on this simple rule is able to create all of the phyllotactic patterns frequently observed in nature. (see Smith et al 2006).

Reaction-diffusion simulation on a growing leaf

The reaction-diffusion models of Gierer and Meinhardt (1982) have been used to model a wide variety of patterning in biology. This movie shows their activator-inhibitor model on a growing leaf. The leaf surface and growth is modeled by key-frame interpolation between Bezier surfaces, the details of which can be found in the supplemental materials of Smith and Bayer 2009.

Patterning mechanism based on auxin transport

Experimental work by the Kuhlemeier group showed that the plant hormone auxin is a key player in organ initiation and phyllotaxis. When auxin feeds back on its own transport, it can create a patterning mechanism that, like reaction-diffusion, is able to break symmetry and create de-novo patterning (see Smith and Bayer 2009 for a review)

A simulation model based on this idea is able to create a variety of the phyllotaxis patterns observed in nature and is described in Smith et al. (2006).

[movie 7 MB]

Up-the-gradient or with-the-flux?

The canalization mechanism for vein formation proposed by Sachs (1981) and modeled by Mitchison (1980) is also thought to be an auxin transport-feedback patterning process. The only primary difference between this mechanism and the one proposed for phyllotaxis is how the auxin transporters orient themselves. The developmental event where these two processes meet is in the formation of the leaf midvein. Here one patterning process seems to seamlessly give way to the other. A simulation model exploring how this might occur can be found in Bayer et al. (2009).

MorphoGraphX: Software for visualization, segmentation, and analysis of 3D image data.

Publications [pdf 470 KB]

• De Rybel, B; Möller, B; Yoshida, S; Grabowicz, I; de Reuille, PB; Boeren, S; Smith, RS; Borst, JW; Weijers, D
  A bHLH Complex Controls Embryonic Vascular Tissue Establishment and Indeterminate Growth in Arabidopsis
  Developmental Cell 24 (4): 426-437 FEB 2013   Reprint

• Routier-Kierzkowska, AL; Smith, RS
  Measuring the mechanics of morphogenesis
  Current Opinion in Plant Biology 16 (1): 25-32 FEB 2013   Reprint

• Vogler, H; Draeger, C; Weber, A; Felekis, D; Eichenberger, C; Routier-Kierzkowska, AL; Boisson-Dernier, A; Ringli, C; Nelson, BJ; Smith, RS; Grossniklaus, U
  The pollen tube: a soft shell with a hard core
  Plant Journal 73 (4): 617-627 FEB 2013    Reprint

• Aegerter-Wilmsen, T; Heimlicher, MB; Smith, AC; de Reuille, PB; Smith, RS; Aegerter, CM; Basler, K
  Integrating force-sensing and signaling pathways in a model for the regulation of wing imaginal disc size
  Development 139 (17): 3221-3231 SEP 2012    Reprint

• Guenot, B; Bayer, E; Kierzkowski, D; Smith, RS; Mandel, T; Žádníková, P; Benková, E; Kuhlemeier, C
  PIN1-Independent Leaf Iinitiation in Arabidopsis thaliana
  Plant Physiology159 (4): 1501-1510 Open Access AUG 2012    Reprint

• Chitwood, DH; Headland, LR; Ranjan, A; Martinez, CC; Braybrook, SA; Koenig, DP; Kuhlemeier, C; Smith, RS; Sinha, NR
  Leaf Asymmetry as a Developmental Constraint Imposed by Auxin-Dependent Phyllotactic Patterning
  Plant Cell 24 (6): 2318-2327 JUN 2012 Open Access   Reprint

• Routier-Kierzkowska, A-L; Weber, A; Kochova, P; Felekis, D; Nelson, B; Kuhlemeier, C; Smith RS
  Cellular Force Microscopy for in vivo Measurements of Plant tissue Mechanics
  Plant Physiology 158 (4): 1514-1522 Open Access APR 2012   Reprint

• Kierzkowski, D; Nakayama, N; Routier-Kierzkowska, A-L; Weber, A; Bayer, E; Schorderet, M; Reinhardt, D; Kuhlemeier, C; Smith, RS
  Elastic Domains Regulate Growth and Organogenesis in the Plant Shoot Apical Meristem
  Science 335 (6072): 1096-1099 MAR 2012   Reprint

• Santuari, L; Scacchi, E; Rodriguez-Villalon, A; Salinas, P; Dohmann, EMN; Brunoud, G; Vernoux, T; Smith, RS; Hardtke, CS
  Positional Information by Differential Endocytosis Splits Auxin Response to Drive Arabidopsis Root Meristem Growth
  Current Biology 21 (22): 1918-1923 NOV 2011   Reprint

• Smith, RS
  Modeling Plant Morphogenesis and Growth. In “New Trends in the Physics and Mechanics of Biological Systems: Lecture Notes of the Les Houches Summer School: Volume 92, July 2009”
  copyright © Oxford University Press, 2011 (preprint)

• Laňková, M; Smith, RS; Pešek, B; Kubeš, M; Zažímalová, E; Petrášek, J; Hoyerová, K
  Auxin influx inhibitors 1-NOA, 2-NOA, and CHPAA interfere with membrane dynamics in tobacco cells
  Journal of Experimental Botany 61 (13): 3589-3598 AUG 2010   Reprint

• Prusinkiewicz, P; Crawford, S; Smith, RS; Ljung, K; Bennett, T;Ongaro, V; Leyser, O
  Control of bud activation by an auxin transport switch
  Proceedings of the National Academy of Science of USA 106 (41): 17431-17436 OCT 2009   Reprint

• Smith RS; Bayer, EM
  Auxin transport-feedback models of patterning in plants
  Plant, Cell & Environment 32 (9): 1258 - 1271 SEP 2009

• Bayer, EM; Smith RS; Mandel, T; Nakayama, N; Sauer, M; Prusinkiewicz, P; Kuhlemeier, C
  Integration of transport-based models for phyllotaxis and midvein formation
  Genes & Development 23 (3): 373 - 384 FEB 2009 supplemental material

• Smith, RS
  The Role of Auxin Transport in Plant Patterning Mechanisms
  PLOS Biology 6 (12) e323: 2631-2633 DEC 2008 Reprint

• Smith, RS; Kuhlemeier, C; Prusinkiewicz, P
  Inhibition fields for phyllotactic pattern formation: a simulation study Source:
  Canadian Journal of Botany, 84 (11): 1635-1649 NOV 2006

• Smith, RS; Guyomarc'h, S; Mandel, T; Reinhardt, D; Kuhlemeier, C; Prusinkiewicz, P
  A plausible model of phyllotaxis
  Proceedings of the National Academy of Sciences USA (PNAS), 103 (5) 1301-1306. JAN 2006