Mechanosensitive control of plant growth: bearing the load, sensing, transducing, and responding

Abstract

As land plants grow and develop, they encounter complex mechanical challenges, especially from winds and turgor pressure. Mechanosensitive control over growth and morphogenesis is an adaptive trait, reducing the risks of breakage or explosion. This control has been mostly studied through experiments with artificial mechanical loads, often focusing on cellular or molecular mechanotransduction pathway. However, some important aspects of mechanosensing are often neglected. (i) What are the mechanical characteristics of different loads and how are loads distributed within different organs? (ii) What is the relevant mechanical stimulus in the cell? Is it stress, strain, or energy? (iii) How do mechanosensing cells signal to meristematic cells? Without answers to these questions we cannot make progress analyzing the mechanobiological effects of plant size, plant shape, tissue distribution and stiffness, or the magnitude of stimuli. This situation is rapidly changing however, as systems mechanobiology is being developed, using specific biomechanical and/or mechanobiological models. These models are instrumental in comparing loads and responses between experiments and make it possible to quantitatively test biological hypotheses describing the mechanotransduction networks. This review is designed for a general plant science audience and aims to help biologists master the models they need for mechanobiological studies. Analysis and modeling is broken down into four steps looking at how the structure bears the load, how the distributed load is sensed, how the mechanical signal is transduced, and then how the plant responds through growth. Throughout, two examples of adaptive responses are used to illustrate this approach: the thigmorphogenetic syndrome of plant shoots bending and the mechanosensitive control of shoot apical meristem (SAM) morphogenesis. Overall this should provide a generic understanding of systems mechanobiology at work.

Keywords: biomechanics; curvature; mechanobiology; mechanotransduction; stress; thigmomorphogenesis; turgor pressure; wind.

Figure 1

Morphological and anatomical structure of a stem submitted to an external bending load from Coutand and Moulia (2000), Journal of Experimental Botany, by permission of the Society for Experimental Biology. (A) Side view of the basal part of the stem base before the application of bending. The stem is grown in hydroponics, and clamped below the primary growth zone, so that bending does not affect its position (Cl, metal clamp; IN 1–3, internodes; Hyp, hypocotyl; Cot, cotyledons. (B) Idealized geometrical scheme (A) as a cantilever beam. (C) Negative photograph of a cross-section (note the quasi-circular shape and the concentric layers of tissues (E, epidermis; Co, collenchyma; Pa, parenchyma; Ph.2, metaphloem; Ca, cambium; Xyl.2, metaxylem; Xyl.1, protoxylem; Ph.i, internal phloem). (D) Changes in the external diameter (●) and of the diameter of the pith (■) along the basal part of the stem.

Figure 2

Structure of the shoot apical meristem (SAM). (A) View of an Arabidopsis thaliana SAM from above Hamant et al. (2008), reprinted with permission from AAAS. (B) Side view of a tomato SAM (Robinson et al., 2013). (C–E) Generalized schematic representations of a typical dome-shaped shoot apex bearing a cylindrical young primordium. (C) Major structures. M, shoot apical meristem; P, organ primordium; B, boundary between the meristem and the primordium. (D) Morphological domains of the SAM. CZ, central zone, PZ, peripheral zone where new organs are generated. (E) Internal organization of the SAM. L1, presumed epidermis, L1 and L2, tunica layers, L3, corpus from Robinson et al. (2013), Journal of Experimental Botany, by permission of the Society for Experimental Biology.

Figure 3

Structure of an integrative structural mechanics (ISM) model from Moulia et al. (2011), by permission of Springer-Verlag Berlin Heidelberg. The structure of an ISM model for use in plant biomechanics. ISM models consider (at least) two scales in the system: a scale of phenomenological empiricism called the material scale, and a scale of mechanistic spatial integration, the mechanical structure. The internal and boundary loads (inputs) result in a change in mechanical state that can be calculated using mechanical principles and robust simplifying theories. ISM models can produce various outputs characterizing mechanical state or dynamics, such as strain (ε) and stress (σ) fields, vibration modes, or rupture risk factors.

Figure 4

The ISM beam model of pure bending of a stem. ISM model used to analyze stem bending experiments, using the theory of composite heterogeneous beams in a cantilever setting. (A) Unloaded beam. The beam is composed of a pile of (virtual) slices of infinitesimal thickness delimited by (virtual) successive cross-sections, along a central line. (B) Loaded beam. Under bending moment $\stackrel{⌢}{M}$(ζ), the beam curves. Each cross-section rotates by a small angle dθ(ζ), with ζ being the position along the stem and x, y the coordinates within the current cross-section of the stem. (C–E) Detailed side (C,D) and top (E) views of a bent slice in a homogeneous stem. (F–H) Detailed side (F,G) and top (H) views of a bent slice in a heterogeneous stem made of one stiff (dark gray) and two compliant (light gray) concentric annuli of tissues. (C,F) Strain distribution across the cross-section. Note that the cross-section remains flat during the bending and only rotates respective to the previous cross-section at the bottom of the slice by an angle dθ, irrespective of the anatomy of the stem. The spatial rate of change in angle of the successive cross-sections is the stem curvature $C=\frac{d\theta }{dS}$. Accordingly, the stem is elongated on the convex side by dl(x, y) > 0 and shortened on the concave side by dl_(x,y) < 0, with no change on the central (neutral) line. The longitudinal strain ${\epsilon }_{LL}=\frac{dl}{dS}$ is thus maximal at the periphery on the sides of the slice that face downwards and away from the orientation of the bending force. The heterogeneous anatomy of the stem has no effect on the relative distribution of strain across the cross-section, which remains linear and is given by ε_LL,y = y · (C − C₀). Straining allows for internal reaction forces, which density is measured by stresses, to build up balancing the effect of the external load. Therefore, the amount of change in stem curvature (and hence the global amount of straining) only depends on the amount of external bending moment and on the overall bending stiffness of the stem. (E,F) Stress distribution in the cross-section. For elastic constituents, the stress is equal to the strain multiplied by the Young's modulus: σ_LL,x,y,i = ε_LL,x,yE_LL,i where E_LL,i is the longitudinal elastic modulus of material i. In homogeneous stems stresses parallel strains. However, on a stem with a heterogeneous anatomy (F) the stresses also depend on the local stiffness of the tissue and they de-correlated with strains across the cross-section (with maximal stresses possibly occurring inside the stem).

Figure 5

The thin-walled pressurized vessel model of the shoot apical meristem. Integrative structural mechanics (ISM) model used to analyze the loading of the SAM by internal turgor pressure, using very thin shell theory (Hamant et al., 2008), reprinted with permission from AAAS. (A) The SAM modeled as a pressurized vessel. Each point has a coordinate in the orthoradial (r) and meridional (s) direction and P is pressure. (B) At the top of the apical dome, represented as a spherical dome, the stress is isotropic. If the flanks of the meristem are represented as a cylinder, the stress is greater in the circumferential (orthoradial) direction than along the meridian and strongly anisotropic stresses occurrs on the flanks of the meristem. Maximal stress anisotropy occurs at the saddle-shaped boundary between the primordium and the central dome.

Figure 6

Finite elements model (FEm) of a patch of the L1 + L2 layer of the SAM. ISM model for the numerical mechanical analysis of a small patch of the SAM with full cellular resolution. The example here displays the model (and the numerical simulation of its stress-field output) of a patch at the boundary between the primordium and the central dome, with the ablation of one L1 cell from Hamant et al. (2008), reprinted with permission from AAAS. (A) General view of the FEm of the patch in the primordium boundary zone from above indicating the simulated pattern of principal stress directions (red lines) on the outer surface of meristem tissue. Colors indicate relative values of stress (blue, low; green, medium; red, high). (B) Side view of the outermost cell layers L1 and L2. (C) Detail of the stress pattern around one hole due to cell ablation.

Figure 7

Local mechanosensing of external loads. (A) Probability of mechanosensitive channel (MsC) opening and mean patch conductance as a function of patch depression (and hence membrane tension and MsC strain). Open and filled circles, two replicates. Dashed dotted line, linear fit. Modified from Ding and Pickard (1993), Copyright# 1993, The Plant Journal, John Wiley and Sons. (B) Relationship between the relative transcript abundance Qr of the primary mechanosensitive gene Pta ZFP2 (measured by Q-RT-PCR) and predictions from the Strain-Sensing model through the volume-averaged strain in the bent stem segment ε, (i.e., Sum of the Strain-Sensing normalized to the volume of the bent tissue; Coutand et al., , Journal of Experimental Botany, by permission of the Society for Experimental Biology).

Figure 8

Mechanosensing of internal loads in the SAM and microtubule re-orientation from Hamant et al. (2008), reprinted with permission from AAAS. (A) Schematic representation of stress directions and microtubule orientations in the different parts of an SAM bearing a cylindrical primordium. (B) Principal stress pattern at the outer surface of the meristem simulated in an FEm of a patch of SAM at the top of the dome with a two-cell ablation. The stress pattern is circumferential to each of the ablated regions and stress alignment is enhanced in the cell between the two ablated cells. (C) Cortical microtubule distribution in the L1 layer in the central zone after a two-cell ablation as visualized by the expression of a construct fusing the Green Fluorescent Protein and the Microtubule Binding Domain (GFP-MBD), Scalebar, 5 μm.

Figure 9

Schematic representation of the SAM Stress Feedback model (SAM SFm). The SAM SFm (Hamant et al., 2008) incorporates an ISM biomechanical model of the mechanical load-bearing structure of the SAM, and a mechanobiological model of the responses to the mechanical state of a cell in terms of (i) cell-wall stress sensing by CMTs and (ii) the consequences on the longitudinal elastic stiffness of the cell wall due to the direction of the laying down of cellulose microfibrils with respect to the longitudinal direction of the cell wall. The elemental brick of the biomechanical model is a piece of cell wall ❶ (called the cell-wall element) which displays two rheological behaviors: (i) elastic straining and (ii) expansion growth changing the rest length l_w,0 of the element at a rate that is proportional to its elastic strain over a certain threshold. Cell wall growth is therefore analogous to visco-plastic creep. The transverse height (d) and thickness (t) of the wall element are assumed to be constant. Two levels of structure can then be assembled. At the first level, ❷ the side walls of a single hexagonal cell are assembled The model can be run at this level, giving rise to the cell-level formulation of the SFm. Otherwise the cells can be assembled to form a surface mesh with typical SAM geometry❸, in the SAM-level formulation of the SFm. The load is the turgor pressure of inner tissues considered to be fully borne by the L1 cell(s) ❹. This ISM biomechanical module outputs the (elastic) wall-stress field σ^e_w at every position X on the different cell-wall elements composing the mechanical structure, at a given time, as well as the changes in rest-lengths of all the cell-wall elements due to expansion growth. This updates the geometry of the cellular structure for the next step and the outputs are transmitted to the mechanobiological module. In the mechanobiological module of the SAM SFm, the mechanosensitive step occurs at the level of the cell ❼, as it is an intrinsic cellular process. The central hypothesis of the module is that CMTs are re-aligned to the current direction of the direction of the resulting stress θc, but this occurs at a constant pace with only some of the overall CMT population (n_cnew) being reoriented during each step (the rate is assumed to be independent of the mechanical state). The current mean orientations of CMTs in two cells sharing a given cell-wall (θ₁(t), θ₂(t)) determines the longitudinal elastic stiffness of the side cell wall E_w presumably through the orientation of the laying down of the new cellulose microfibrils with respect to the existing wall, changing the anisotropy of the cell wall elastic rigidity and hence its longitudinal stiffness (here assumed to be instantaneous) ❻ (note that (θ₁(t), θ₂(t)) may differ from the targeted orientations (θc₁, θc₂) specified by the stress-feedback as CMT reorientation takes time). The latter process occurs at the level of each cell-wall element so different walls of the same cell differ in the amount of elastic stiffening they undergo. The new value of wall elastic stiffness E_w is the output of the mechanosensitive module and is transferred to the mechanical module, in which the elastic stiffness is updated, immediately changing the constitutive law of the cell walls, and thus giving rise to a new mechanical equilibrium at the next step. This change in wall elastic rigidity is the way the current wall-stress state feeds back on the growth of the meristematic cells. Note that cell division may occur (not shown). A phragmoplast (new cell wall) is laid down parallel to the current CMT direction θ1 whenever the size of the stem passes a certain size threshold thereby changing the structure of the L1 cell wall “mesh.”

Figure 10

Schematic representation of thigmomorphogenetic model including the ISM beam model and the S³m. The ISM model of the mechanical load-bearing structure (left) is the CBmS designed by Coutand and Moulia (2000) to analyze stem bending experiments (see Figure 3). It is based on a validated composite-beam model of plant organ flexion (Moulia and Fournier, 1997). In its most simple configuration its inputs are the curvature field C(ζ) and the bending moment M(ζ) along the stem (measured as in Moulia et al., 1994). Its parameters are: (i) length, L, and diameters along the stem, D(ζ); (ii) estimates of tissue stiffness (longitudinal Young's moduli Coutand and Moulia, 2000); and (iii) the anatomical cross-sectional images processed using the model by Moulia and Fournier (1997). The elementary unit is a piece of tissue assumed to behave in the linear elastic range. Like all models based on beam-theory, this model defines two integration levels: the cross-section (which can be heterogeneous) and the stem. From the curvature field, it computes the strain field, ε(x, y, ζ, t) (and the stress field σ(x, y, ζ, t) if required) with ζ being the position along the stem and x,y the coordinates within the current cross-section of the stem, and t the time. The mechanosensitive model is the S³m model (Moulia et al., 2011). Its inputs are the strain fields ε(x, y, ζ, t) in each stem, and the stem geometry factors L and D(ζ), (all these data are received from the ISM beam model). S³m then generates the local sensing in a tissue element, and, if needed, the predicted amount of transcription Qr of a primary mechanosensitive gene. Then the integrated secondary signals S_i,1 and S_i,2 reaching the primary and secondary meristems, respectively, are computed. These signals are inputs of a module of thigmomorphogenetic growth responses (Coutand and Moulia, ; Coutand et al., 2009) outputting logarithmic dose-response modulations of primary and secondary growth. In a fully-coupled dynamic model of thigmomorphogenesis, the outputs of the thigmomorphogenetic growth response module can be used to update the size and geometry of the stem at the next step, so time integration can be simulated.

Figure 11

Experimental assessment of the S³m model. Dose-response curve of the recovery time of the primary growth response after bending plotted against the candidate internal signal (S_1,strains) predicted by the S³m model (adapted from Coutand and Moulia, Journal of Experimental Botany, by permission of the Society for Experimental Biology). (A) A logarithmic relationship is obtained under the hypothesis that the mechanosensed variable is the strain and which explains 72% of the overall response. (B) No relationship is obtained under the hypothesis that the mechanosensed variable is the stress. —, log fit; ♦, experimental results.

Figure 12

Experimental assessment of the 2D Stress Feedback model (SFm) of the entire morphogenetic dynamics of the SAM from Hamant et al. (2008), reprinted with permission from AAAS. (A) marking cortical microtubules (green) and cell shape (red) at the surface of a meristem generating a young primordium (P). Cortical microtubule marking is obtained using the expression of a fusion protein involving the Green Fluorescent Protein and the Microtubule Binding Domain (GFP-MBD) under the control of the constitutive promoter 35S (p35S::GFP-MBD) Scale bar, 20 mm. (B) Microtubule orientation (red bars) in cells in the 2D SFm (extracted from confocal data). Note the alignment of the virtual microtubule orientations in the boundary zone and compare to (A). (C) Simulation of an auxin-induced primordium. The 2D SFm results in orthoradial alignment of microtubules around the growing primordium. (D) Tip-growing simulation with the stress-feedback model generating a growing stem. Microtubules align mainly orthoradially in the stem, which has a regular shape.

Figure 13

S³m-assisted dissection of natural genetic diversity in mechanosensing. Relationship between the standardized diametric growth responses of five neotropical forest species and the log of the candidate internal signal (S_2,strain) predicted by the S³m model. S_2,strain = sum of strains over the cross-section during the bending treatment from Coutand et al. (2010), Annals of Botany, by permission of Oxford University Press.