A multiphysics model for rapid collapse and slow recovery movements of Mimosa pudica with experimental validation

• Main Author: Wang, Yifeng
• Other Authors: Li Hua
• Format: Thesis-Doctor of Philosophy
• Language: English
• Published: Nanyang Technological University 2021
• Subjects: Engineering::Mechanical engineering::Bio-mechatronics
• Online Access: https://hdl.handle.net/10356/148516
• Institution: Nanyang Technological University

A remarkable feature of Mimosa pudica is its ability to deform rapidly in response to certain external stimuli. In this thesis, a two-dimensional(2D) transient bio-chemo-electro-mechanical model of the rapid collapse movement of the main pulvinus of Mimosa pudica is developed. Based on the laws of mass and momentum conservations and theories of poroelasticity and representative volume elements, novel equations for fluid pressure, water channel, ionic pump, and hygro-morphic behaviour are proposed to characterize the cell elasticity and deformation. Experiments are also conducted to measure the time, amplitude, and triggering force of the rapid collapse and the slow recovery movements. After examinations with published experiments, it is confirmed that the model can predict well the ionic concentrations, petiole collapse movement, pulvinus deformation, mechanosensitive action potential, and membrane potential, and the relevant contributions are summarized below. The study in this thesis explores the fundamental mechanism of the Mimosa pudica movement and will serve for developing novel bio-inspired stimuli-responsive actuators. As the first achievement of the present work, the experiment is conducted for the rapid collapse and slow recovery movements of Mimosa pudica, in terms of the main pulvinus diameter, bending angle, movement time, mechanical triggering force, and stem position. The petiole bending angle and movement time are measured when subject to various types of stimulations, including mechanical, electrical, and light-illumination stimulations. The experiments for circadian rhythm and fatigue phenomenon are also conducted for the repeatability of Mimosa pudica recovery movement. As the second achievement in thesis, a 2D model is developed theoretically for the rapid collapse movement of Mimosa pudica with the bio-chemo-electro-mechanical coupled field. The model is validated with experiments for ionic diffusion, water redistribution, and considerable deformation. The model consists of governing equations for the mass conservation and provides a detailed description of the electrochemical transport of solute. Based on the governing equations over plant tissue, the model also deals with both symplastic and apoplastic transporting pathways with diffusion and convection terms. The mechanical deformation of pulvinus cross section is then handled by the formulations of mechanical force equilibrium, constitutive and kinematic equations by solid mechanics. The bio-chemo-electro-mechanical multiple energy fields are numerically solved by coupling the diffusion model for water and multiple ions, the solid mechanics, and the poroelasticity multiphysics. Based on the Poisson-Nernst-Planck equations and Darcy’s law in plant physiology, the model simulates the hydrostatic-osmotic-driven fluid pressure, nonlinear diffuse-poroelasticity, and semi-permeability of the cell membrane. The bio-chemo-electro-mechanical multiple energy fields are numerically solved by coupling the diffusion model for ions and water, the porous media model for plant tissue, and the elasticity model for cytoplasm and cell walls. Osmotic pressure is computed based on the concentration of various ionic species, and hydrostatic pressure mechanically on the cortex volume containing the cytoskeleton and water. The main pulvinus is considered as a cylindrical structure with hundreds of extensor and flexor motor cells. Distributive ionic and water transportations are simulated upon the activation of ionic and water channels, and then osmotic pressure difference is characterised, resulting in mechanical deformation of motor cells. Apart from that, simulation results are compared well with the present experiment for the effects of environmental conditions, as well as with published experiments for ionic concentrations, collapse movement, epidermis displacement and membrane potential in the main pulvinus. Several case studies are carried out for the effects of plant morphogenesis such as maturity and senescence, and plant biophysical properties such as hydrostatic pressure, pore surface fraction, cell wall stiffness, and pulvinus diameter. The results and discussions highlight the biochemical actuation mechanism of the Mimosa pudica movement and confirm the importance of ionic and water transports for causing changes in osmotic and hydrostatic pressures. As the third achievement made in this thesis, the slow recovery movement of Mimosa pudica the main pulvinus is modeled by the extension of the above bio-chemo-electro-mechanical model, to estimate the variability of critical parameters in the recovery of motor cells and open probability for water flux. The turgor pressure is characterised in the apoplast during the cell plasmolysis process, subject to the activation of ionic and water channels, resulting in mechanical deformation of Mimosa pudica eventually. The model is extended by adding the Lockhart-Ortega and Goldman equations for the simulations of (i) the biological sensitivity of cell membrane via micro-scaled opening and closing of water and ionic transport in channels, with variable cell elastic modulus and required free energy for mechanosensitive activation (ii) the signal transduction in motor cells via mechanosensitive action potential, and (iii) the recovery of the motor organ via an instant step down or up of turgor pressure within the apoplast. The deformation of the motor organ is thus determined by a combination of ionic and water transport in the channel, signal transduction in membrane assembly, and the balance of turgor pressure in the single-cell recovery. The extended model is validated through comparison with reported experiments, and good agreements are achieved regarding both 2D ionic redistribution and reuptake and recovery deformation of pulvinus cross section, in terms of water distribution, extensor volume change, and mechanosensitive action potential. Several case studies are also carried out for the turgor pressure, bending angle and elastic modulus of Mimosa pudica, subject to various water diffusion coefficients, pore surface fractions, ionic and water concentrations, pulvinus diameters, and cell volumetric modulus. In conclusion, the water diffusion coefficient play main roles in the recovery of Mimosa pudica movement. The ionic and water channels are also important for cell volume change, osmotic and hydrostatic pressures, resulting in a closed feedback loop mediated by in turgor pressure. The extended model is also deduced to two analytical solutions for two experimental situations: DC stimulation and electroneutrality. The results are compared with numerical simulation and previous model. The present numerical method is the only one that predicts both collapse and recovery movements.