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Plant Sciences


Systems Biology/Developmental Modeling

Model of a raspberry created with L-systems

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
[movie 18 MB]

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.

Reaction-diffusion growing leaf
[movie 4 MB]

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).

Lucas phyllotaxis
[movie 16 MB]
Bijugate phyllotaxis
[movie 6 MB]
We have since been able to generate even more patterns!

Dual Model
[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).

All models shown on this page were built using the L-studio software created by Prof. Przemyslaw Prusinkiewicz and his Biological Modeling and Visualization group at the University of Calgary.

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

Publications [pdf 470 KB]

Asst. Prof. Dr. Richard S. Smith

Richard S. Smith

University of Bern
Plant Sciences
Altenbergrain 21
CH-3013 Bern
Phone: +41 31 631 5223
Fax: +41 31 631 4942
Annelise Routier
Anne-Lise Routier
Pierre Barbier de Reuille
Pierre Barbier de Reuille
Alain Weber
Alain Weber
Gabriella Mosca
Gabriella Mosca
Michal Huflejt
Michal Huflejt
Agatha Burian
Agata Burian
 Are you interested in joining us?

MSc studentships

Growth and mechanical properties of Tobacco culture cells

Simulation model of a growing Arabidopsis root tip in 3D


Tim Rudge
Tim Rudge

Petra Kochova
Petra Kochova

Funding generously provided by

University of Bern

SystemsX – PGCE


Scientific Exchange Programme NMS-CH

Swiss National Science Foundation

Distichous Decussate Tricussate Fibonacci