Mathematical principles and models of plant growth mechanics: from cell wall dynamics to tissue morphogenesis

Smithers, Euan T; Luo, Jingxi; Dyson, Rosemary

doi:10.1093/jxb/erz253

“…[Oscillatory ion movement in the electrolyte solution (Pietruszka et al 2018) accompanies the uni-directional increase in pollen tube, and changes the chemical potential (Fermi redox energy) of particular ions]. Further investigations can go along the lines clearly illustrated in Smithers et al (2019).…”

Section: Final Commentsmentioning

confidence: 99%

Chemical Potential-Induced Wall State Transitions in Plant Cell Growth

Pietruszka

¹

2019

J Plant Growth Regul

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The pH/T duality of acidic pH and temperature (T) action for the growth of grass shoots was examined in order to derive the phenomenological equation of wall properties for living plants. By considering non-meristematic growth as a dynamic series of state transitions (STs) in the extending primary wall, the critical exponents were identified, which exhibit a singular behaviour at a critical temperature, critical pH and critical chemical potential (μ) in the form of four power laws: $$f_{\pi } \left( \tau \right) \propto \left| \tau \right|^{\beta - 1}$$ f π τ ∝ τ β - 1 , $$f_{\tau } (\pi ) \propto \left| \pi \right|^{1 - \alpha }$$ f τ ( π ) ∝ π 1 - α , $$g_{\mu } (\tau ) \propto \left| \tau \right|^{ - 2 - \alpha + 2\beta }$$ g μ ( τ ) ∝ τ - 2 - α + 2 β and $$g_{\tau } (\mu ) \propto \left| \mu \right|^{2 - \alpha }$$ g τ ( μ ) ∝ μ 2 - α . The indices α and β are constants, while π and τ represent a reduced pH and reduced temperature, respectively. The convexity relation α + β ≥ 2 for practical pH-based analysis and β ≡ 2 “mean-field” value in microscopic (μ) representation were derived. In this scenario, the magnitude that is decisive is the chemical potential of the H+ ions, which force subsequent STs and growth. Furthermore, observation that the growth rate is generally proportional to the product of the Euler beta functions of T and pH, allowed to determine the hidden content of the Lockhart constant Ф. It turned out that the pH-dependent time evolution equation explains either the monotonic growth or periodic extension that is usually observed—like the one detected in pollen tubes—in a unified account.

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“…A recent study using onion epidermal wall concluded that tensile (in-plane) properties (elastic compliance, plastic compliance, and creep) were largely determined by the network of cellulose microfibrils within individual lamellae of this polylamellate wall, whereas the indentation (out-of-plane) properties were largely controlled by pectins, along with some contributions from the cellulose microfibril networks (Zhang et al , 2019). Such results need to be incorporated into quantitative cell wall models with both explanatory and predictive value (Smithers et al , 2019).…”

Section: Discussionmentioning

confidence: 99%

Pectin methylesterase selectively softens the onion epidermal wall yet reduces acid-induced creep

Wang

¹

,

Cosgrove

²

2019

Preprint

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De-esterification of homogalacturonan (HG) is thought to stiffen pectin gels and primary cell walls by increasing calcium crosslinking between HG chains. Contrary to this idea, recent studies found that HG de-esterification correlated with reduced stiffness of living tissues, measured by surface indentation. The physical basis of such apparent wall softening is unclear, but possibly involves complex biological responses to HG modification. To assess the direct physical consequences of HG de-esterification on wall mechanics without such complications, we treated isolated onion (Allium cepa) epidermal walls with pectin methylesterase (PME) and assessed wall biomechanics with indentation and tensile tests. In nanoindentation assays, PME action softened the wall (reduced the indentation modulus). In tensile force/extension assays, PME increased plasticity, but not elasticity. These softening effects are attributed, at least in part, to increased electrostatic repulsion and swelling of the wall after PME treatment. Despite softening and swelling upon HG de-esterification, PME treatment alone failed to induce cell wall creep. Instead, acid-induced creep, mediated by endogenous α expansin, was reduced. We conclude that HG de-esterification physically softens the onion wall, yet reduces expansin-mediated wall extensibility.HighlightAfter enzymatic de-esterification without added calcium, the onion epidermal wall swells and becomes softer, as assessed by nanoindentation and tensile plasticity tests, yet exhibits reduced expansin-mediated creep.

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“…The factors partially involved in anisotropic growth are multiple and are not limited to cytoskeleton configuration. Cell elongation is mainly driven by two mechanisms: cell wall deformation by internal turgor pressure and cell wall growth mediated by enzymatic reactions [involving expansins, xyloglucan endotransglucosylase/hydrolase (XTH), and pectin-modifying enzymes (PMEs)] and favored by hormones accumulation (like auxin, gibberellins and abscisic acid; Cosgrove, 2016 ; Smithers et al, 2019 ). The latter is commonly known as the acid growth hypothesis ( Figure 1B ; Rayle and Cleland, 1992 ).…”

Section: Grasping On the Complexity Of Plant Organ Structurementioning

confidence: 99%

Shaping the Organ: A Biologist Guide to Quantitative Models of Plant Morphogenesis

Marconi

¹

,

Wabnik

²

2021

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Organ morphogenesis is the process of shape acquisition initiated with a small reservoir of undifferentiated cells. In plants, morphogenesis is a complex endeavor that comprises a large number of interacting elements, including mechanical stimuli, biochemical signaling, and genetic prerequisites. Because of the large body of data being produced by modern laboratories, solving this complexity requires the application of computational techniques and analyses. In the last two decades, computational models combined with wet-lab experiments have advanced our understanding of plant organ morphogenesis. Here, we provide a comprehensive review of the most important achievements in the field of computational plant morphodynamics. We present a brief history from the earliest attempts to describe plant forms using algorithmic pattern generation to the evolution of quantitative cell-based models fueled by increasing computational power. We then provide an overview of the most common types of “digital plant” paradigms, and demonstrate how models benefit from diverse techniques used to describe cell growth mechanics. Finally, we highlight the development of computational frameworks designed to resolve organ shape complexity through integration of mechanical, biochemical, and genetic cues into a quantitative standardized and user-friendly environment.

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Mathematical principles and models of plant growth mechanics: from cell wall dynamics to tissue morphogenesis

Cited by 44 publications

References 94 publications

Chemical Potential-Induced Wall State Transitions in Plant Cell Growth

Chemical Potential-Induced Wall State Transitions in Plant Cell Growth

Pectin methylesterase selectively softens the onion epidermal wall yet reduces acid-induced creep

Shaping the Organ: A Biologist Guide to Quantitative Models of Plant Morphogenesis

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