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

Abstract

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.

The stomatal flexoskeleton: how the biomechanics of guard cell walls animate an elastic pressure vessel

“…In computational modeling studies, guard cell-neighbor interactions are modeled as distributed loads (pressure) from neighboring cells on the guard cells (Cooke et al, 1976;Woolfenden et al, 2017;Yi et al, 2018) or are not explicitly considered (Marom et al, 2017). Thus, there is no consensus on the magnitude and importance of the biomechanical influence of neighboring cells on guard cells during stomatal opening and closure.…”

“…Despite recent advances in our ability to build computational models of complex geometries, seemingly idealized geometric shapes are often used to model stomatal complexes. For example, more recent computational modeling studies have used symmetric and well-defined geometric shapes (Cooke et al, 2008;Carter et al, 2017;Marom et al, 2017;Woolfenden et al, 2017Woolfenden et al, , 2018. However, close observation of reconstructed 3D images of stomatal complexes reported in Zhao and Sack (1999), Meckel et al (2007), and Yi et al (2018) reveals that stomatal complexes are not all identical and are neither perfectly symmetrical nor perfectly elliptical or toroidal.…”

“…Recent research has focused on understanding how plants construct guard cell walls that are strong enough to withstand high turgor pressure (measured as high as 5 MPa) and yet flexible enough to repeatedly expand and shrink. Most of these studies have focused on the thickness and mechanical properties of guard cell walls (Carter et al, 2017;Marom et al, 2017;Woolfenden et al, 2017Woolfenden et al, , 2018Yi et al, 2018). Studies concerning those two aspects are reviewed below, highlighting their biomechanical implications.…”

“…Therefore, deformation needs to be accounted for during calculations of the loads that result in the final geometry of the complex in response to stimuli. In a modern computational modeling environment, this is achieved by considering the geometric non-linearity of the stomatal complex (Marom et al, 2017;Woolfenden et al, 2017;Yi et al, 2018).…”

“…As pointed out by Yi et al (2018) and Marom et al (2017), understanding the geometric configuration of a stomatal complex and its interaction with neighboring cells is important for explaining how the specific deformation patterns of stomatal guard cells facilitate the opening and closure of the stomatal pore. Acknowledging that stomatal behavior is a collective response of multiple elements such as stomatal complex shape, guard cell shape, cell wall morphology, interactions between sister guard cells and their neighboring subsidiary or pavement cells, and the mechanical properties of guard cell walls that reflect their molecular structures, it is imperative to account for the implications of any assumptions, idealizations, and/or simplifications employed during analysis of experimental and modeling data.…”