Ashwani Goel

Viscoelastic properties of cell walls of single living plant cells determined by dynamic nanoindentation

Plant development results from controlled cell divisions, structural modifications, and reorganizations of the cell wall. Thereby, regulation of cell wall behaviour takes place at multiple length scales involving compositional and architectural aspects in addition to various developmental and/or environmental factors. The physical properties of the primary wall are largely determined by the nature of the complex polymer network, which exhibits time-dependent behaviour representative of viscoelastic materials. Here, a dynamic nanoindentation technique is used to measure the time-dependent response and the viscoelastic behaviour of the cell wall in single living cells at a micron or sub-micron scale. With this approach, significant changes in storage (stiffness) and loss (loss of energy) moduli are captured among the tested cells. The results reveal hitherto unknown differences in the viscoelastic parameters of the walls of same-age similarly positioned cells of the Arabidopsis ecotypes (Col 0 and Ws 2). The technique is also shown to be sensitive enough to detect changes in cell wall properties in cells deficient in the activity of the chromatin modifier ATX1. Extensive computational modelling of the experimental measurements (i.e. modelling the cell as a viscoelastic pressure vessel) is used to analyse the influence of the wall thickness, as well as the turgor pressure, at the positions of our measurements. By combining the nanoDMA technique with finite element simulations quantifiable measurements of the viscoelastic properties of plant cell walls are achieved. Such techniques are expected to find broader applications in quantifying the influence of genetic, biological, and environmental factors on the nanoscale mechanical properties of the cell wall.

Creating micro- and nanostructures on tubular and spherical surfaces

The authors developed a new technique to create micro- and nanometer scale structures on curved free-standing objects by combining embossing/imprinting lithography approaches with mechanical loadings on elastic films. Embossing/imprinting generates small structures and mechanical loading determines shape or geometry of the final object. As a result, a portion of the tubes with a radius between 0.5 and 3.5 mm and a portion of the spheres with a radius between 2.4 and 7.0 mm were fabricated with grating line features (period of 700 nm) and microlens array features (lens radius of 2.5 μm) atop, respectively. It was found that both static analyses and finite element models can give good estimates on the radii of those curved objects, based on the dimension of the two layers, loading format, as well as mechanic strains. Thus, good control over shape and dimension of the free-standing structure can be achieved.

In vivo extraction of Arabidopsis cell turgor pressure using nanoindentation in conjunction with finite element modeling.

Turgor pressure in plant cells is involved in many important processes. Stable and normal turgor pressure is required for healthy growth of a plant, and changes in turgor pressure are indicative of changes taking place within the plant tissue. The ability to quantify the turgor pressure of plant cells in vivo would provide opportunities to understand better the process of pressure regulation within plants, especially when plant stress is considered, and to understand the role of turgor pressure in cellular signaling. Current experimental methods do not separate the influence of the turgor pressure from the effects associated with deformation of the cell wall when estimates of turgor pressure are made. In this paper, nanoindentation measurements are combined with finite element simulations to determine the turgor pressure of cells in vivo while explicitly separating the cell-wall properties from the turgor pressure effects. Quasi-static cyclic tests with variable depth form the basis of the measurements, while relaxation tests at low depth are used to determine the viscoelastic material properties of the cell wall. Turgor pressure is quantified using measurements on Arabidopsis thaliana under three pressure states (control, turgid and plasmolyzed) and at various stages of plant development. These measurements are performed on cells in vivo without causing damage to the cells, such that pressure changes may be studied for a variety of conditions to provide new insights into the biological response to plant stress conditions.

Geometrically Exact Nonlinear Extended-Reissner/Mindlin Shells: Fundamentals, Finite Element Formulation, Elasticity

Extended Reissner/Mindlin shell kinematics are used to develop an exact shell that makes no further approximations on the deformation or strain. The formulation is fully tensorial. A three-dimensional isoparametric element is used as the reference configuration. The FE approximation introduces nodes on the mid-surface of the isoparametric element, with the thickness having a separately defined interpolation. The variational formulation is based on the nominal stress tensor. Isotropic linear and nonlinear elastic shells are constructed that use p-type interpolation along the director. The formulation is exact, resulting in nonlinear elements showing better characteristics in comparison to other such elements.