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Central limit theorem and the short-term temperature response of coleoptile and hypocotyl elongation growth

100%
Lewicka S., Pietruszka M.
Acta Societatis Botanicorum Poloniae
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2008
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tom 77
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nr 4
289-292
In this contribution we deal with a new mathematical description of the response of short-term coleoptile/hypocotyl expansion growth to temperature. Although the interest of both the bio-mechanical basis of elongation growth and temperature responses has been studied in plant biology and biophysics for a long time, yet the question of the mode of actions of temperature is very relevant and still open. Here we introduce a simple idea that the normal distribution, due to the central limit theorem (CLT), is able to report on temperature-dependent elongation growth. The numerical fittings for temperature affected growth are in good agreement with empirical data. We suggest that the observation concerning a crossover effect occurring in temperature driven elongation together with CLT leads to the formulation of a hypothesis about the possible universal character of such a description, supposedly for many plant species and families. We conclude with the statement that properly constructed equations of temperature affected growth, should possibly include a specific term proportional to exp[-((T-T0)/T0)2] with T0 corresponding to the temperature of the optimum growth.
2
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Mathematical model for tissue stresses in growing plant cells and organs

100%
Lewicka S., Pietruszka M.
Acta Societatis Botanicorum Poloniae
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2009
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tom 78
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nr 1
19-23
In this study we propose a simple mathematical model based on the equilibrium equation for the materials deformed elastically. Owing to the turgor pressure of the cells, the peripheral walls of the outer tissue are under tension, while the extensible inner tissue is under compression. This well known properties of growing multicellular plant organs can be derived from the equation for equilibrium. The analytic solutions may serve as a good starting point for modeling the growth of a single plant cell or an organ.
3
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Thermodynamics of irreversible plant cell growth

80%
Pietruszka M., Lewicka S., Pazurkiewicz-Kocot K.
Acta Societatis Botanicorum Poloniae
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2006
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tom 75
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nr 3
183-190
The time-irreversible cell enlargement of plant cells at a constant temperature results from two independent physical processes, e.g. water absorption and cell wall yielding. In such a model cell growth starts with reduction in wall stress because of irreversible extension of the wall. The water absorption and physical expansion are spontaneous consequences of this initial modification of the cell wall (the juvenile cell vacuolate, takes up water and expands). In this model the irreversible aspect of growth arises from the extension of the cell wall. Such theory expressed quantitatively by time-dependent growth equation was elaborated by Lockhart in the 60's.The growth equation omit however a very important factor, namely the environmental temperature at which the plant cells grow. In this paper we put forward a simple phenomenological model which introduces into the growth equation the notion of temperature. Moreover, we introduce into the modified growth equation the possible influence of external growth stimulator or inhibitor (phytohormones or abiotic factors). In the presence of such external perturbations two possible theoretical solutions have been found: the linear reaction to the application of growth hormones/abiotic factors and the non-linear one. Both solutions reflect and predict two different experimental conditions, respectively (growth at constant or increasing concentration of stimulator/inhibitor). The non-linear solution reflects a common situation interesting from an environmental pollution point of view e.g. the influence of increasing (with time) concentration of toxins on plant growth. Having obtained temperature modified growth equations we can draw further qualitative and, especially, quantitative conclusions about the mechanical properties of the cell wall itself. This also concerns a new and interesting result obtained in our model: We have calculated the magnitude of the cell wall yielding coefficient (T) [m3 J-1•s-1] in function of temperature which has acquired reasonable numerical value throughout.
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