Modelling plant cell expansion in VirtualLeaf
11 June 2015
Campus Middelheim (CMI), building G, room G.005 - Middelheimlaan 1 - 2020 Antwerpen
Organization / co-organization:
Faculty of Sciences
J. Broeckhove & G. Beemster
PhD defence Abdiravuf Dzhurakhalov - Faculty of Sciences
At the cellular and subcellular levels the mechanical properties of cell walls have a direct influence on cell size, shape and expansion as well as the cell's water relations. From a higher perspective they regulate the mechanics of the whole plant tissue as well as other aspects of plant development.
The aim of this study is the construction of realistic models for plant cell wall mechanics describing correctly the wall elasticity, plasticity and viscoelasticity, and the extension of the capabilities of the VirtualLeaf software framework. In this regard, the following contributions to the field of computer-based simulation, in particular, to the VirtualLeaf framework have been achieved:
A more robust criterion for Monte Carlo (MC) energy minimization method in VirtualLeaf was developed where a use of gradient norm is impossible due to multivariable and complex systems. This sliding window criterion is based on the continuous checking a threshold value within some energy difference window sliding along the energy change of the system. In this method the correctness of finding a stable state increases drastically in comparison with a single value method used in original VirtualLeaf.
A parameter exploration of MC calculation of Hamiltonian has been performed. A robust method based a MC evolution of total energy during equilibration cycle was elaborated for choosing the good values of MC parameters. It was shown that the values of parameters found in this way were optimal for the fast reaching the equilibrated state.
An Elastic Wall method of Hamiltonian has been developed and implemented in VirtualLeaf. In this method the whole wall between cells is used in Hamiltonian instead of its. In this new approach the individual resting lengths for each wall were introduced. Using the wall is physically correct in relation of its whole extension/compression than the local changing within one of its edges.
Irreversible deformation of wall has been improved by introducing a threshold turgor pressure (as in Lockhart equation) instead of the threshold wall length and a continuous irreversible deformation of wall with growth rate instead of existing one time-step edge/wall yield in VirtualLeaf. Elastic Wall method and a new irreversible deformation approach have been validated with experimental data on the maize leaf tissue expansion.
To better describe the cell wall mechanics a Maxwell's viscoelastic model, in which the wall deformation is determined by the combination of Hooke's law and Newton's law, has been introduced in VirtualLeaf. This model is time dependent: the rest length of each wall and the turgor pressure in each cell are updated at each time step by solving an ordinary differential equation.
In this way the capabilities of VirtualLeaf platform to study the mechanical basis of growth in plant organs such as leaves and roots have been extended. Preliminary tests show that these new implemented models describe very well cell wall mechanics in plant cells.