Project

Modeling of the development of Arabidopsis flowers

Flower formation is an intricate process that occurs through a series of sequential steps. The process starts with ‘floral induction’ : the apical meristem cells switch from a vegetative to a reproductive state when floral-meristem identity genes are activated by an external floral stimulus.

The next step is ‘floral development’: the floral meristem is patterned into the whorls of organ primordia, which receive their identities through the activity of floral-organ identity genes. Eventually, the latter genes activate downstream effectors that specify the various tissues and cell types of the flower. In the flowering process, the proteins belonging to the dimerizing MADS box transcription factor family play an essential role. In fact, flowering is governed by the dynamics of the network they constitute. For Arabidopsis, the potential MADS box protein-protein interactions have to a great extent been unraveled  and with ‘floral induction’ and ‘flower development’  different subnetworks are associated. However, these subnetworks are not independent, but coupled by negative feedback interactions.



Example of a highly simplified model (for purpose of demonstration) with two MADS box proteins and two dimers.
Example of a highly simplified model (for purpose of demonstration) with two MADS box proteins and two dimers.


As for the ‘floral development’ step, the so-called ABC combinatorial model of gene expression states predicts the identity of floral organ primordia. The ABC model itself does not provide an explanation of how the necessary steady state patterns of gene expression characteristics are attained and maintained through gene interactions. A model in terms of differential equations has been developed that describes the dynamics of the MADS proteins in time. The parameters in this model have been fit to data from the literature. By integrating this model one finds the time development of the protein concentrations determining the fate of the apical meristem cells. The reliability of this model has been checked using mutant data and the model predictions fit remarkably well with experimental observations.

A second aspect of this project is the development of a model that describes auxin transport in the floral meristem. High auxin concentrations are believed to act as triggers for primordial development. The positions, numbers, and time ordering of the auxin peaks following from model simulations agree to a  great extend with the positions of the Arabidopsis primordia.

This on-going project is done in cooperation with: A.D.J. van Dijk, G.H. Immink, K. Kaufmann, G.C. Angenent, R.C.H.J. van Ham, and S. Urbanus.


Project output

Publications in International peer-reviewed journals

  • Simon van Mourik*, G. Wilma van Esse*, Hans Stigter, Colette A. ten Hove, Jaap Molenaar, Sacco C. de Vries (2012). A Mathematical Model for BRASSINOSTEROID INSENSITIVE1-Mediated Signaling in Root Growth and Hypocotyl Elongation. Plant Physiology, 160 (1), 523-532. *contributed equally
  • S. van Mourik, K. Kaufmann, A.D.J. van Dijk, G.C. Angenent, R.M.H. Merks, J. Molenaar (2012). Integrating two patterning processes in the flower. Addendum to: Simulation of organ patterning on the floral meristem using a polar auxin transport model. Plant Signaling & Behavior 7(6) 1-3.
  • Simon van Mourik, Dirk Vries, Johan P.M. Ploegaert, Hans Zwart, Karel J. Keesman (2012). Physical parameter estimation in spatial heat transport models with an application to food storage. Biosystems Engineering, 112(1), 14-21.
  • A.D.J. van Dijk, S. van Mourik, R.C.H.J. van Ham (2012). Mutational Robustness of Gene Regulatory Networks. PLoS ONE 7(1).
  • S. van Mourik, K. Kaufmann, A.D.J. van Dijk, G.C. Angenent, R.M.H. Merks, J. Molenaar (2012). Simulation of Organ Patterning on the Floral Meristem Using a Polar Auxin Transport Model. PLoS ONE 7(1).
  • Simon van Mourik, Aalt D.J. van Dijk, Maarten de Gee, Richard G.H. Immink, Kerstin Kaufmann, Gerco C. Angenent, Roeland C.H.J. van Ham, and Jaap Molenaar (2010). Continuous-time modeling of cell fate determination in Arabidopsis flowers. BMC Systems Biology, 4:101. Selected for the Faculty of 1000.
  • S. van Mourik, H. Zwart, K.J. Keesman (2010). Switching input controller for a food storage room. Control Engineering Practice 18(5), 507-514.
  • H.J. Zwart, S. van Mourik, K.J. Keesman (2010). Switching control for a class of non-linear systems with an application to post-harvest food storage. European Journal of Control, 16(5), 567-573.
  • S. van Mourik, B. Geurts, H. Zwart, K.J. Keesman (2010). Modelling and Controller Design for a UV Disinfection Plant. European Journal of Control, 16(2), 1-10.
  • S. van Mourik, H. Zwart, K.J. Keesman (2009). Integrated Open Loop Control And Design Of A Food Storage Room. Biosystems Engineering, 104 (4), 493-502.
  • S. van Mourik, H. Zwart, K.J. Keesman (2009). Modelling and controller design for distributed parameter systems via residence time distribution. International Journal of Control, 82 (8) 1404-1413.
  • S. van Mourik, A.E.P. Veldman and M. Dreyer (2005). Simulation of capillary flow with a dynamic contact angle. Microgravity Science and Technology, 17(3), 91-98.

Dutch National reviewed journals

  • S. van Mourik en A.E.P. Veldman (2005). Rollende vloeistof, Nieuw Archief voor de Wiskun­de, vijfde serie, 6(2), 124-129.

Reviewed conference proceedings

  • Simon van Mourik, Joris Bierkens, Hans Stigter, Martijn Dirkse, Karel Keesman, and Vivi Rottschäfer (2009). DHV water pumping optimization, Proc. of the 67th European Study Group Mathematics with Industry, Wageningen.
  • K.J. Keesman, D. Vries, S. van Mourik, and H. Zwart (2007). Modeling and control of water disinfection process in annular photoreactors. Proc. of the European Control Conference, Kos (Greece).
  • Vincent Creigen, Luca Ferracina, Andriy Hlod, Simon van Mourik, Krischan Sjauw, Vivi Rottschäfer, Michel Vellekoop, and Paul Zegeling (2007). Modeling a heart pump. Proc. of the 58th European Study Group Mathematics with Industry, Utrecht, 7-25.
  • Simon van Mourik, Yves van Gennip, Mark Peletier, Andriy Hlod, Vadim Shcherbakov, Peter in ’t panhuis, Erwin Vondenhoff, Pieter Eendebak, and Jan Bouwe van den Berg (2006). Catching gas with droplets. Proc. of the 55th European Study Group Mathematics with Industry, Eindhoven, 69-100.
  • Marcus Tindall, Mark Peletier, Joyce Aitchison, Simon van Mourik, and Natascha Severens (2005). The mathematical modelling of cooling and re-warming patients during cardiac surgery. Proc. of the 52nd European Study Group Mathematics with Industry, Amsterdam, 39-51.
  • M.R. Opmeer, F.W. Wubs and S. van Mourik (2005), Model reduction for controller design for infinite-dimensional systems: theory and example. Proc. of the 44th IEEE Conference on Decision and Control, Sevilla (Spain), 2469-2474.

Theses

  • Modelling and control of systems with flow (2008). Ph.D. Thesis. University of Twente. ISBN 978-90-365-2617-3.
  • LQG balancing in controller design (2003). M.Sc. thesis. University of Groningen.
  • Numerical modelling of the dynamic contact angle (2002). M.Sc. thesis. University of Groningen.