Abstract
We have developed an algorithm for a particle-based model for the growth of plant tissues in three dimensions in which each cell is represented by a single particle, and connecting cell walls are represented as permanent bonds between particles. A sample of plant tissue is represented by a fixed network of bonded particles. If, and only if a cell divides, this network is updated locally. The update algorithm is implemented in a model where cell growth and division gives rise to forces between the cells, which are relaxed in steepest descent minimization. The same forces generate a pressure inside the cells, which moderates growth. The local nature of the algorithm makes it efficient computationally, so the model can deal with a large number of cells. We used the model to study the growth of plant tissues for a variety of model parameters, to show the viability of the algorithm.
Highlights
The basic building blocks of all higher organisms are biological cells
An important distinction between plant and animal cells is that plant cells are connected to each other by the middle lamella, a pectin layer formed at cell division
Because it irreversibly glues the cells together, plant tissues consist of a permanent network of cells, the topological structure of which only changes upon cell division
Summary
The basic building blocks of all higher organisms are biological cells. The growth, morphology and functionality of the organisms are based upon the growth, division and interaction between the cells. The model we present for the developing cell network in plant tissue is based upon the molecular or Brownian dynamics simulation techniques from physics and chemistry These techniques describe particles interacting via potentials. Sozinova et al [6] use a similar model to study bacterial clustering, taking into account the shape of the bacteria Both models are particle based, and very much simpler than our model, giving extremely fast simulations, but they are not applicable to plant tissue. The cellular Potts model (CPM) as developed by Graner & Glazier [7] derives from the classical Potts model in statistical mechanics, developed to describe phenomena in solid-state physics It treats cells as a collection of points on a regular lattice, and is a widely used and very efficient model to describe a relatively small number of cells, including their dynamical shape and internal structure. For a complete overview of the various models and methods, we refer to these 3 review papers
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