Software developed in the mathematical biology group

For our computational research on collective cell behavior during biological development, we routinely develop simulation codes that we are releasing as open source. If you plan to model animal tissues, use Tissue Simulation Toolkit, a two-dimensional implementation of the Cellular Potts Model. If you want to model plant tissues, please use our vertex-based cell-based simulation software VirtualLeaf.

Apart from developing our own codes for the Cellular Potts Model, we have used the excellent open source package CompuCell3D. The Tissue Simulation Toolkit is a relatively small and straightforward C++ library, making it well suited for developing new ideas and algorithms. CompuCell3D is well suited for constructing new biological models based on existing technology and minor extensions in the form of ``plugins''.


Tissue Simulation Toolkit

Tissue Simulation Toolkit 2.0 (TST 2.0) is a two-dimensional library for the Cellular Potts Model (Graner and Glazier 1992; Phys. Rev. Lett. 69, 2013), which is increasingly used by computational biologists to study tissue patterning and developmental mechanisms. The current release of TST contains many new features, including:

TST 2.0 provides many recent extensions to the CPM, including:
  • Efficient edgelist algorithm
  • Infinite number of PDE layers (forward Euler)
  • A reacion diffusion solver on the CPU and on CUDA
  • Interaction of CPM cells and PDE (secretion, absorption)
  • Chemotaxis
  • Length and connectivity constraints
  • Act-CPM model (Niculescu et al., PLOS Comput Biol 2015)
  • Interaction with discrete fibrous extracellular matrix, based on coupling to HOOMD-Blue, as developed in Tsingos, Bakker et al. Biophysical Journal 2023

The recent version of the TST, and in particular the coupling with HOOMD-Blue contains many optimizations developed by, and in collaboration with the TissueOpt project of the eScience Center.

Download the Tissue Simulation Toolkit 2.0 software here, or first check the documentation.

Papers on Tissue Simulation Toolkit


We first mentioned the tissue simulation toolkit in: R M H Merks, & J A Glazier. (2005). A cell-centered approach to developmental biology. Physica A, 352(1), 113–130. doi:10.1016/j.physa.2004.12.028. Please cite that paper and the Github repositor if you use the TST in your work.

A detailed step by step tutorial is published in Josephine T. Daub and Roeland M. H. Merks (2015) Cell-based computational modeling of vascular morphogenesis using Tissue Simulation Toolkit. In: Vascular Morphogenesis. Domenico Ribatti (Ed.) Methods in Molecular Biology, 1214: 67-127. link

Papers using Tissue Simulation Toolkit

  • Martijn de Jong, Esmée Adegeest, Noémie M.L.P. Bérenger-Currias, Maria Mircea, Roeland M.H. Merks, Stefan Semrau (2024) The shapes of elongating gastruloids are consistent with convergent extension driven by a combination of active cell crawling and differential adhesion. PLOS Computational Biology 20(2): e1011825. (https://doi.org/10.1371/journal.pcbi.1011825)
  • Vroomans, R.M.A., Colizzi, E.S. Evolution of selfish multicellularity: collective organisation of individual spatio-temporal regulatory strategies. BMC Ecol Evo 23, 35 (2023). https://doi.org/10.1186/s12862-023-02133-x
  • Erika Tsingos, Bente Hilde Bakker, Koen A.E. Keijzer, Hermen Jan Hupkes & Roeland M.H. Merks Hybrid cellular Potts and bead-spring modeling of cells in fibrous extracellular matrix (2023) Biophysical Journal 122(13): 2609-2622 https://doi.org/10.1016/j.bpj.2023.05.013
  • Enrico Sandro Colizzi, Renske M.A. Vroomans, Roeland M.H. Merks (2022) Evolution of multicellularity by collective integration of spatial information. eLife 2020;9:e56349 https://doi.org/10.7554/eLife.56349
  • Leonie van Steijn, Inge M.N. Wortel, Clément Sire, Loïc Dupré, Guy Theraulaz, Roeland M.H. Merks (2022) Computational modelling of cell motility modes emerging from cell-matrix adhesion dynamics. PLOS Computation Biology 18(2): e1009156 (https://doi.org/10.1371/journal.pcbi.1009156)
  • Elisabeth G. Rens, Mathé T. Zeegers, Iraes Rabbers, András Szabó, Roeland M. H. Merks (2020)  Autocrine inhibition of cell motility can drive epithelial branching morphogenesis in absence of growth. Philosophical Transactions B, 375: 20190386 (doi:10.1098/rstb.2019.0386). (Preprint at bioRxiv, doi:10.1101/2020.05.15.088377)
  • Szabó A, Theveneau E, Turan M, Mayor R (2019) Neural crest streaming as an emergent property of tissue interactions during morphogenesis. PLOS Computational Biology 15(4): e1007002. doi:10.1371/journal.pcbi.1007002
  • Szabó, A., Melchionda, M., Nastasi, G., Woods, M. L., Campo, S., Perris, R., Mayor, R. (2016). In vivo confinement promotes collective migration of neural crest cells. Journal of Cell Biology, 213(5), 543-555.doi:10.1083/jcb.201602083
  • Niculescu I, Textor J, de Boer RJ (2015) Crawling and Gliding: A Computational Model for Shape-Driven Cell Migration. PLOS Computational Biology 11(10): e1004280. doi:10.1371/journal.pcbi.1004280
  • Hannan Tahir, Ioana Niculescu, Carles Bona-Casas, Roeland M.H. Merks, Alfons G. Hoekstra (2015) An in-silico study on the role of smooth muscle cells migration in neointimal formation after coronary stenting. Journal of the Royal Society Interface 12: 20150358. doi:10.1098/rsif.2015.0358
  • Daub, J. T., & Merks, R. M. H. (2013). A cell-based model of extracellular-matrix-guided endothelial cell migration during angiogenesis. Bull Math Biol, 75(8), 1377–1399. doi:10.1007/s11538-013-9826-5
  • Szabó, A., Varga, K., Garay, T., Hegedűs, B., & Czirok, A. (2012). Invasion from a cell aggregate--the roles of active cell motion and mechanical equilibrium. Physical Biology, 9(1), 016010–016010. doi:10.1088/1478-3975/9/1/016010
  • Szabó, A., Unnep, R., Méhes, E., Twal, W. O., W S Argraves, Cao, Y., & A Czirók. (2010). Collective cell motion in endothelial monolayers. Physical Biology, 7(4), 046007. doi:10.1088/1478-3975/7/4/046007
  • Scianna, M., Roeland M H Merks, Preziosi, L., & Medico, E. (2009). Individual cell-based models of cell scatter of ARO and MLP-29 cells in response to hepatocyte growth factor. Journal of Theoretical Biology, 260(1), 151–160. doi:10.1016/j.jtbi.2009.05.017
  • Szabó, A., & Czirok, A. (2010). The Role of Cell-Cell Adhesion in the Formation of Multicellular Sprouts. Mathematical Modelling of Natural Phenomena, 5(1), 106–122. doi:10.1051/mmnp/20105105
  • Merks, R. M. H., Perryn, E. D., Shirinifard, A., & Glazier, J. A. (2008). Contact-inhibited chemotaxis in de novo and sprouting blood-vessel growth. PLoS Comp Biol, 4(9), e1000163. doi:10.1371/journal.pcbi.1000163
  • Szabó, A., Mehes, E., Kosa, E., & Czirok, A. (2008). Multicellular sprouting in vitro. Biophysical Journal, 95(6), 2702–2710. doi:10.1529/biophysj.108.129668
  • Savill, N. J., & Merks, R. M. H. (2007). The Cellular Potts Model in Biomedicine. In A. R. A. Anderson, M. A. J. Chaplain, & K. A. Rejniak, Single-Cell-Based Models in Biology and Medicine (pp. 137–150). Birkhaüser Verlag.
  • Merks, R. M. H., Brodsky, S. V., Goligorksy, M. S., Newman, S. A., & Glazier, J. A. (2006). Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling. Developmental Biology, 289(1), 44–54. doi:10.1016/j.ydbio.2005.10.003
  • Merks, R. M. H., & Glazier, J. A. (2006). Dynamic mechanisms of blood vessel growth. Nonlinearity, 19(1), C1–C10. doi:10.1088/0951-7715/19/1/000
  • Merks, R. M. H., Newman, S. A., & Glazier, J. A. (2004). Cell-oriented modeling of in vitro capillary development. Lect. Notes Comput. Sci., 3305, 425–434.

VirtualLeaf

VirtualLeaf is a cell-based computer-modeling framework for plant tissue morphogenesis. The current version defines a set of biologically-intuitive C++ objects, including cells, cell walls, and diffusing and reacting chemicals, that provide useful abstractions for building biological simulations of developmental processes. VirtualLeaf-based models provide a means for plant researchers to analyze the function of developmental genes in the context of the biophysics of growth and patterning. The VirtualLeaf runs on Windows, Mac and Linux.

Overview


VirtualLeaf is a cell-based computer-modeling framework for plant tissue morphogenesis. The current version defines a set of biologically-intuitive C++ objects, including cells, cell walls, and diffusing and reacting chemicals, that provide useful abstractions for building biological simulations of developmental processes. VirtualLeaf-based models provide a means for plant researchers to analyze the function of developmental genes in the context of the biophysics of growth and patterning. The VirtualLeaf runs on Windows, Mac and Linux.

Papers on VirtualLeaf, including user manuals

If you use VirtualLeaf in your work, please cite our paper:

  • Merks, R. M. H., Guravage, M., Inzé, D., & Beemster, G. T. S. (2011). VirtualLeaf: An Open-Source Framework for Cell-Based Modeling of Plant Tissue Growth and Development. Plant Phys., 155(2), 656–666. (Open Access)

A step-by-step introduction to building models with the VirtualLeaf, providing basic example models for Gierer-Meinhardt systems, leaf venation and meristem development, is available in:

  • Claudiu-Cristi Antonovici, Guacimo Y. Peerdeman, Harold B. Wolff, Roeland M. H. Merks (2022) Modeling Plant Tissue Development Using VirtualLeaf. In: Mikaël Lucas (Ed.), Plant Systems Biology: Methods and Protocols, series Methods in Molecular Biology book series (MIMB, volume 2395), pp. 165-198. doi:10.1007/978-1-0716-1816-5_9

This chapter is the updated edition of:

  • Merks, R. M. H., & Guravage, M. A. (2012). Building Simulation Models of Developing Plant Organs Using VirtualLeaf. In Methods in Molecular Biology (Vol. 959, pp. 333–352). doi: 10.1007/978-1-62703-221-6_23 preprint.

If you need assistance in setting up parameter studies for your model, please see our chapter:

We have extended VirtualLeaf with cell sliding, allowing simulation of confluent animal tissues. See:

  • Henri B. Wolff, Lance A. Davidson* and Roeland M.H. Merks* (* co-corresponding authors). Adapting a plant tissue model to animal development: introducing cell sliding into VirtualLeaf. Bulletin of Mathematical Biology (2019). doi: 10.1007/s11538-019-00599-9. The source code of this extension is available on request.

Recent new features developed by Richard van Nieuwenhoven, Ruth Großeholz and Bruno Hay Mele included cell sliding and cell wall remodeling algorithms, differential cell wall thickness and importing of SVG images as initial conditions. These new features are available in the most recent Github repository and they are documented in the following preprint:

  • Ruth Großeholz, Richard W. van Nieuwenhoven*, Bruno Hay Mele, and Roeland M.H. Merks (preprint) Enhanced Cell Wall Mechanics in VirtualLeaf Enable Realistic Simulations of Plant Tissue Dynamics. bioRxiv: 2024.08.01.605200. doi: 10.1101/2024.08.01.605200 (* corresponding author)

Publications using VirtualLeaf

  • Ivan Lebovka, Bruno Hay Mele, Xiaomin Liu, Alexandra Zakieva, Theresa Schlamp, Nial Rau Gursanscky, Roeland MH Merks, Ruth Großeholz, Thomas Greb (2023) Computational modeling of cambium activity provides a regulatory framework for simulating radial plant growth. eLife 12:e66627. doi: 10.7554/eLife.66627
  • Aimée R. Kok (2023) An extension for virtualleaf to explore the mechanical division rule in plant morphogenesis. MSc Thesis, Wageningen University. eDepot Wageningen University, nr. 636816
  • Jonathan E. Dawson, Abby Bryant, Trevor Jordan, Simran Bhikot, Shawn Macon, Breana Walton, Amber Ajamu-Johnson, Paul D. Langridge, Abdul N. Malmi-Kakkada (preprint) Synthetic Notch Activation Patterns in a Proliferating Tissue. bioRxiv: 2023.07.12.548752. doi: 10.1101/2023.07.12.548752
  • David M Holloway, Carol L Wenzel (2021) Polar auxin transport dynamics of primary and secondary vein patterning in dicot leaves in silico Plants 3:2, diab030 doi: 10.1093/insilicoplants/diab030
  • Irina Kneuper, William Teale, Jonathan Edward Dawson, Ryuji Tsugeki, Eleni Katifori, Klaus Palme, Franck Anicet Ditengou (2021) Auxin biosynthesis and cellular efflux act together to regulate leaf vein patterning, Journal of Experimental Botany, 72(4), 1151–116510.1093/jxb/eraa501
  • Francesco Giannino, Bruno Hay Mele, Veronica De Micco, Gerardo Toraldo, Stefano Mazzoleni, Fabrizio Cartenì (2019) An Individual Based Model of Wound Closure in Plant Stems. IEEE Access, 7, 65821-65827, doi: 10.1109/ACCESS.2019.2915575.
  • Henri B. Wolff, Lance A. Davidson* and Roeland M.H. Merks* (* co-corresponding authors). Adapting a plant tissue model to animal development: introducing cell sliding into VirtualLeaf. Bulletin of Mathematical Biology (2019). doi: 10.1007/s11538-019-00599-9
  • Dirk De Vos, Abdiravuf Dzhurakhalov, Sean Stijven, Przemyslaw Klosiewicz, Gerrit T. S. Beemster, Jan Broeckhove (2017) Virtual Plant Tissue: Building Blocks for Next-Generation Plant Growth Simulation. Frontiers in Plant Science, 8:686. doi: 10.3389/fpls.2017.00686
  • Irina Kneuper, William Teale, Jonathan Edward Dawson, Ryuji Tsugeki, Klaus Palme, Eleni Katifori, Franck Anicet Ditengou (2017) Tissue specific auxin biosynthesis regulates leaf vein patterning. bioRxiv: 184275 doi: 10.1101/184275
  • Elise Kuylen, Gerrit TS Beemster, Jan Broeckhove, Dirk De Vos (2017) Simulation of regulatory strategies in a morphogen based model of Arabidopsis leaf growth. Simulation of regulatory strategies in a morphogen based model of Arabidopsis leaf growth. Procedia Computer Science 108C, 139-148. doi: 10.1016/j.procs.2017.05.238
  • Mellor, N., Adibi, M., El-Showk, S., De Rybel, B., King, J., Mähönen, A.P., Weijers, D., Bishopp, A. (2016) Theoretical approaches to understanding root vascular patterning: a consensus between recent models. J Exp Bot, advanced acces. doi:10.1093/jxb/erw410
  • Dzhurakhalov, A. (2015). Modelling plant cell expansion in VirtualLeaf. PhD Thesis. University of Antwerp. http://gradworks.umi.com/36/64/3664579.html
  • De Rybel, B., Adibi, M., Breda, A. S., Wendrich, J. R., Smit, M. E., Novák, O., et al. (2014). Integration of growth and patterning during vascular tissue formation in Arabidopsis. Science (New York, NY), 345(6197), 1255215–1255215. doi:10.1126/science.1255215
  • Draelants, D., Avitabile, D. & Vanroose, W. (2015) Localised auxin peaks in concentration-based transport models for plants. J. Roy. Soc. Interface 12(106):20141407. doi:10.1186/1752-0509-4-98
  • Dirk De Vos, Emil De Borger, Jan Broeckhove, Gerrit TS Beemster (2015) Simulating leaf growth dynamics through Metropolis-Monte Carlo based energy minimization. Journal of Computational Science, 9: 107-111. doi: 10.1016/j.jocs.2015.04.026
  • A Dzhurakhalov, D De Vos, G Beemster and J Broeckhove (2015) Monte Carlo parameterization in the VirtualLeaf framework. Journal of Physics: Conference Series, 640: 012012. doi: 10.1088/1742-6596/640/1/012012
  • De Vos D, Vissenberg K, Broeckhove J, Beemster GTS (2014) Putting Theory to the Test: Which Regulatory Mechanisms Can Drive Realistic Growth of a Root?. PLOS Computational Biology 10(10): e1003910. doi: 10.1371/journal.pcbi.1003910.
  • Van Mourik, S., Kaufmann, K., Van Dijk, A. D. J., Angenent, G. C., Merks, R. M. H., & Molenaar, J. (2012). Simulation of Organ Patterning on the Floral Meristem Using a Polar Auxin Transport Model. PLoS ONE, 7(1), e28762. doi:10.1371/journal.pone.0028762.s018
  • Dzhurakhalov AA, De Vos D, Vanroose W, Beemster GTS, Broeckhove J (2012) Implementation of realistic cell wall mechanics in VirtualLeaf. 7th Plant Biomechanics International Conference, Clermont-Ferrand, August 2012.
  • Wabnik, K., Kleine-Vehn, J., Balla, J., Sauer, M., Naramoto, S., Reinöhl, V., et al. (2010). Emergence of tissue polarization from synergy of intracellular and extracellular auxin signaling. Molecular Systems Biology, 6, 447. doi: 10.1038/msb.2010.103
  • R M H Merks, Van de Peer, Y., Inzé, D., & Beemster, G. T. S. (2007). Canalization without flux sensors: a traveling-wave hypothesis. Trends in Plant Science, 12(9), 384–390. doi: 10.1016/j.tplants.2007.08.004

Downloads

Recent downloads can be obtained from Github: https://github.com/rmerks/VirtualLeaf2021