Modelling plant cell expansion in VirtualLeaf

At the cellular level the mechanical properties of cell walls have a direct influence on cell size, shape and expansion as well as the cell's water relations. 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.;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 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 edges. 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) and a continuous irreversible deformation of wall with growth rate 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 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.