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发布于:2018-2-10 02:35:31  访问:3 次 回复:0 篇
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By virtue of their target locations. {This is
Cell walls behave as elastic springs with vertically 2’,3,4,4’-tetrahydroxy Chalcone biological activity oriented walls contributing less to the energy function (typically scaled down 5 or 10 times). Model simulations do allow assessment of root growth rate and size, as well as detailed kinematics (the latter is in pri.By virtue of their target locations. This really is mathematically expressed as terms inside a generalized power function (or `Hamiltonian‘), which was slightly modified to represent balanced linear development (in the sense that little cells contribute equally for the energy function as larger cells, if they have identical relative growth rates). Original Hamiltonian: H lA Xi(i){AT (i) zlMXj(j){LT (j)Where indices i and j sum over all cells and polygon edges, respectively, lA is a parameter setting the cells‘ resistance toIn Silico Kinematics of the Arabidopsis Rootcompression or expansion, and lM is a spring constant. AT is the cell‘s target area, LT the wall element target length. In the new Hamiltonian the first term is replaced by: X a(i){AT (i)ilAa(i)The cell mechanics algorithm in VirtualLeaf randomly displaces all nodes to steer the system towards a global energy minimum. During this Metropolis Monte Carlo simulation any node displacement that leads to an energy decrease (or a small energy increase corresponding to a high Boltzmann probability) is accepted [25]. Added example input xml files contain the mechanical and numerical integration settings for simulation and illustrate the data structure used to describe the state of the cellular grid (Dataset S1). Besides the mechanical framework cells and cell walls are endowed with biochemical properties represented by reaction and transport equations and logical rules that determine when and how cell division occurs and how the cellular surface energy terms change. Our approach is to alter the structure of those equations and rules rather than just change parameter values to compare the output of the model versions. The cellular organisation of the root tip was inspired by an earlier study [12] and always starts from a regular grid of rectangular cells, sometimes with narrower inner cell layers roughly in accordance to root anatomical characteristics [7]. The upper cell row always consisted of fixed nodes to enforce downward growth. Across all simulations the three lowest cell rows are not driven to grow in size (via their fixed target areas) and are meant to represent the complex of columella cells together with the quiescent centre (QC). Although this part of the root apex (root cap) has its own detailed developmental characteristics, we strictly focus here on the proximal/basal side of the QC while excluding the distal meristem as part of the growth process. The formative asymmetric divisions of the stem cells surrounding the QC [74] were neither included. The models in principle describe growth in two dimensions but it was assumed that transversal expansion is severely constrained, which is in correspondence with experimental data indicating little or no tangential expansion (,1 h21: [75]). Cell walls behave as elastic springs with vertically oriented walls contributing less to the energy function (typically scaled down 5 or 10 times). This is sufficient to allow fluent elongation of cells along the root axis while keeping cell shape adequately constrained as required by turgor pressure acting on the cell walls.
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