Stomatal Opening: The Role of Cell-Wall Mechanical Anisotropy and Its Analytical Relations to the Bio-composite Characteristics

Stomata are pores on the leaf surface, which are formed by a pair of curved, tubular guard cells; an increase in turgor pressure deforms the guard cells, resulting in the opening of the stomata. Recent studies employed numerical simulations, based on experimental data, to analyze the effects of various structural, chemical, and mechanical features of the guard cells on the stomatal opening characteristics; these studies all support the well-known qualitative observation that the mechanical anisotropy of the guard cells plays a critical role in stomatal opening. Here, we propose a computationally based analytical model that quantitatively establishes the relations between the degree of anisotropy of the guard cell, the bio-composite constituents of the cell wall, and the aperture and area of stomatal opening. The model introduces two non-dimensional key parameters that dominate the guard cell deformations-the inflation driving force and the anisotropy ratio-and it serves as a generic framework that is not limited to specific plant species. The modeling predictions are in line with a wide range of previous experimental studies, and its analytical formulation sheds new light on the relations between the structure, mechanics, and function of stomata. Moreover, the model provides an analytical tool to back-calculate the elastic characteristics of the matrix that composes the guard cell walls, which, to the best of our knowledge, cannot be probed by direct nano-mechanical experiments; indeed, the estimations of our model are in good agreement with recently published results of independent numerical optimization schemes. The emerging insights from the stomatal structure-mechanics "design guidelines" may promote the development of miniature, yet complex, multiscale composite actuation mechanisms for future engineering platforms.