Probing stress-regulated ordering of the plant cortical microtubule array via a computational approach
Functional properties of cells, tissues, and organs rely on predictable growth outputs. A shape change in plant cells is determined by properties of a tough cell wall that deforms anisotropically in response to high turgor pressure. This morphogenesis requires tight coordination and feedback controls among cytoskeleton-dependent wall patterning, its material properties, and stresses in the wall. Cortical microtubules bias the mechanical anisotropy of cell wall by defining the trajectories of cellulose synthase motility as they polymerize bundled microfibrils in their wake. Cortical microtubules could locally align and orient relative to cell geometry; however, the means by this orientation occurs is not known. Correlations between the microtubule orientation, cell geometry, and predicted tensile forces are strongly established, and here we simulate how different attributes of tensile force can orient and pattern the microtubule array in the cortex. We implemented a discrete model with three-state transient microtubule behaviors influenced by local mechanical stress in order to probe the mechanisms of stress-dependent patterning. We varied the sensitivity of four types of dynamic behaviors observed on the plus ends of microtubules - growth, shrinkage, catastrophe, and rescue - to local stress and then evaluated the extent and rate of microtubule alignments in a square computational domain. We optimized constitutive relationships between local stress and the plus-end dynamics and employed a biomechanically well-characterized cell wall to analyze how stress can influence the density and orientation of microtubule arrays. Our multiscale modeling approaches predict that spatial variability in stress magnitude and anisotropy mediate mechanical feedback between the wall and organization of the cortical microtubule array. Author SummaryPlant cell growth involve multiple steps and processes. During growth, cell shape changes continuously while responding to external cues from the surroundings. Since growth is mainly driven by pressure, mechanical properties of cell wall are crucial in regulating multiple biological processes that underlie cell expansion and growth. Cell wall assembly is dynamically coupled to the remodeling of subcellular proteins. Experimental evidence has confirmed there exists potential mechanical feedback between wall assembly and protein-protein interactions. However, the actual mechanism remains unknown. In this study, we develop a computational model to study how mechanical stress could affect subcellular protein dynamics or interactions and lead to their reorganization, reminiscent of continuous changes in global pattern and cell morphology. Our results identify key parameters that can respond to external mechanical stimuli at the cellular scale. We also show that a biological stress pattern could induce protein filament organization and bundles that mimic real subcellular structure from experimental images. These computational results could benefit design of experiments for studying and discovering the potential protein candidates that underlie the mechanical feedback between multiple cellular components. In this way, a more systematic understanding about plant cell growth could be achieved, with an integrated theory that combine biology, chemistry, mechanics, and genetics.