On the Relation between Turgor Pressure and Tissue Rigidity. I

Falk, Stig Olof; Hertz, C. H.; Virgin, Hemming I.

doi:10.1111/j.1399-3054.1958.tb08274.x

Cited by 120 publications

(71 citation statements)

References 7 publications

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“…e was 78 bar, a.Air was 7 bar. (22), and (c) indirectly by measurement of tissue rigidity (13). Each method has its own advantages and disadvantages which must be carefully considered.…”

Section: Discussionmentioning

confidence: 99%

Analysis of the Dynamic and Steady-State Responses of Growth Rate and Turgor Pressure to Changes in Cell Parameters

Cosgrove

1981

Plant Physiol.

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The physical analysis of plant cell enlargment is extended to show the dependence of turgor pressure and growth rate under steady-state cond dons on the parameters which govern ceil wall extension and water transport In growing ceUls and tissues, and to show the dynamic responses of turgor and growth rate to instantaneous changes In one of these parameters. The analysis is based on the fact that growth requires simultaneons water uptake and irreversible wail expansion. It shows that when a growing ceU is perturbed from its steady-state growth rate, it will approach the steady-state rate with exponential kinetics. The half-time of the transient adjustment depends on the biophysical parameters governing both water transport and irreversible wail expansion. When wall extensibility is smal compared to hydraulic conductance, the growth rate is controLbd by the yielding properties of the ceUl wall, while the half-time for changes in growth rate is controlled by the water transport parameters. The reverse situation occurs when hydraulic conductance is iower than wall extensibility. The analysis also shows explicitly that turgor pressure is tightly coupled with growth rate when growth is controlled by both water transport and wall yieling parameters.In growing tissue where the resistance to water flow is distributed throughout the tissue, the physical analysis is more complicated because gradients in water potential (and hence turgor pressure) are required to sustain high growth rates. However, the analysis of growth in such tissues shows that the turgor and time-course relations are similar to that in single cells. These turgor and time-course relations provide experimentally useful ways for determining (a) whether growth is limited by water uptake, and (b) whether an agent which alters the growth rate does so by affecting the water transport or wall yielding properties or both.The enlargement of plant cells is considered to be due to the irreversible yielding of the cell wall to the stress produced by cell turgor (17, 26). In its simplest form, the theory states that two simultaneous processes are required for cell enlargement: (a) water uptake and (b) irreversible expansion of the cell wall. In principle, either one of these processes may limit growth. The theory was first put into explicit analytical form by Lockhart (20) who derived an expression relating the steady-state growth rate to the physical parameters which control water transport and wall expansion. This concept of turgor-driven wall extension has been supported by numerous experimental results (3,7,14,15,27).

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“…e was 78 bar, a.Air was 7 bar. (22), and (c) indirectly by measurement of tissue rigidity (13). Each method has its own advantages and disadvantages which must be carefully considered.…”

Section: Discussionmentioning

confidence: 99%

Analysis of the Dynamic and Steady-State Responses of Growth Rate and Turgor Pressure to Changes in Cell Parameters

Cosgrove

1981

Plant Physiol.

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“…This is especially true for thin-walled, living tissues (e.g. parenchyma and collenchyma) whose stiffness can change in response to cell turgor (Falk et al, 1958 ;Greenberg et al, 1989 ;Niklas, 1989 ;Niklas & Paolillo, 1997). Because the stiffness of organic structures, such as leaves, also depends on which tissues (and how much of each) are present, ontogenetic and phylogenetic variations in leaf stiffness are expected regardless of whether fundamental anatomical differences exist across clades or whether transient physiological changes occur.…”

Section: Leaf Biomechanicsmentioning

confidence: 99%

A mechanical perspective on foliage leaf form and function

1999

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The mechanical behaviour of large foliage leaves in response to static and dynamic mechanical forces is reviewed in the context of a few basic engineering principles and illustrated in terms of species drawn from a variety of vascular plant lineages. When loaded under their own weight or subjected to externally applied forces, petioles simultaneously bend and twist, and thus mechanically operate as cantilevered beams. The stresses that develop in petioles reach their maximum intensities either at their surface or very near their centroid axes, where they are accommodated either by living and hydrostatic tissues (parenchyma and collenchyma) or dead and stiff tissues (sclerenchyma and vascular fibres) depending on the size of the leaf and the species from which it is drawn. Allometric analyses of diverse species indicate size-dependent variations in petiole length, transverse shape, geometry and stiffness that accord well with those required to maintain a uniform tip-deflection for leaves with laminae differing in mass. When dynamically loaded, the laminae of many broad-leaved species fold and curl into streamlined objects, thereby reducing the drag forces that they experience and transmit to their subtending petioles and stems. From a mechanical perspective, the laminae of these species operate as stress-skin panels that distribute point loads more or less equally over their entire surface. Although comparatively little is known about the mechanical structure and behaviour of foliage leaves, new advances in engineering theory and computer analyses reveal these organs to be far more complex than previously thought. For example, finite-element analyses of the base of palm leaves reveal that stresses are decreased when these structures are composed of anisotropic as opposed to isotropic materials (tissues).

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“…The cross-sections of two stems (E. canadensis and P. pectinatus) resembled circular shapes; however, the coefficient b for E. canadensis was 1.60, and the structure of this species was denser than that of P. pectinatus (Figure 3). Thus, E. canadensis had a lower volume of air channels, which may result in lower turgor pressure, which, in turn, affects the stem stiffness [56]. The impact of the shape on the final outcomes in this species, therefore, was smaller than in P. pectinatus due to higher elasticity [35,36].…”

Section: Discussionmentioning

confidence: 93%

On the Relationship between Aquatic Plant Stem Characteristics and Drag Force: Is a Modeling Application Possible?

Łoboda

Karpiński

Bialik

2018

Water

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This paper presents a basic model that shows the relationship between the diameter of a stem and its flexural rigidity. The model was developed from experimental measurements of biomechanical traits (i.e., tensile and bending traits like maximum forces, stresses, moduli of elasticity, flexural rigidity, strain) of three freshwater macrophyte species (Elodea canadensis Michx., Potamogeton pectinatus L., and P. crispus L.), reflecting the seasonal changes in plant biomechanics throughout the vegetative season. These were obtained with the use of a bench-top testing machine in 2016 and 2017. The presented calculations are based on the ratio of drag-to-bending forces, in which the flexural rigidity plays a key role. The proposed model has the form EI = ad b , and two approaches based on a regression analysis were applied to determine the parameters of the model-a and b. In the first method, the parameters were identified separately for each day of measurement, while in the second method, the coefficient b was calculated for all data from all days as a unified number for individual plants. The results suggest that coefficient b may provide information about the proportion of changes in drag forces depending on plant stiffness. The values of this coefficient were associated with the shape of the stem cross-section. The more circular the cross-section, the closer the value of the parameter was to 1. The parameter values were 1.60 for E. canadensis, 1.98 for P. pectinatus, and 2.46 for P. crispus. Moreover, this value also depended on the density of the cross-section structure. Most of the results showed that with an increase in stem diameter, the ratio between the drag and bending forces decreased, which led to fewer differences between these two forces. The model application may be introduced in many laboratory measurements of flow-biota interactions as well as in aquatic plant management applications. The implementation of these results in control methods for hydrophytes may help in mitigating floods caused by increases to a river channel's resistance due to the occurrence of plants.

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On the Relation between Turgor Pressure and Tissue Rigidity. I

Cited by 120 publications

References 7 publications

Analysis of the Dynamic and Steady-State Responses of Growth Rate and Turgor Pressure to Changes in Cell Parameters

Analysis of the Dynamic and Steady-State Responses of Growth Rate and Turgor Pressure to Changes in Cell Parameters

A mechanical perspective on foliage leaf form and function

On the Relationship between Aquatic Plant Stem Characteristics and Drag Force: Is a Modeling Application Possible?

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